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		ДОСРОЧНЫЙ ЕГЭ 28.04.2014
1		Найдите наибольшее значение функции y = (x − 27 ) e28 − x на отрезке[23;40]. maximize (x-27)*E^(28-x) over [23,40]
2		y = (x − 4 ) e2x − 7 →  [2;11] minimize (x-4)*E^(2*x-7) over [2,11]
3		y = (2 x − 6 ) e13 −4 x →  [2;14]. maximize (2*x-6)*E^(13-4*x) over [2,14]
4		y = (2 x +15 ) e2 x + 16 →  [−12;−2] minimize (2*x+15)*E^(2*x+16) over [-12,-2]
		ЭКСТРЕМУМЫ ЛОКАЛЬНЫЕ И ГЛОБАЛЬНЫЕ
		ТОЧКА МИНИМУМА Найдите точку минимума функции
▲		y = x3 − 48 x + 17 local minima x^3-48x+17 local extrema x^3-48x+17 d(x^3-48x+17)/dx>=0
▲		y = x3 − 3 x2 + 2 local minima x^3-3x^2+2
▲		y = x3 − 2 x2 + x + 3 local minima x^3-2x^2+x+3
▲		y = x3 + 5 x2 + 7 x − 5 local minima x^3+5x^2+7x-5
▲		y = 7 + 12 x −x3 local minima -x^3+12x+7
▲		y = 9 x2 −x3 local minima -x^3+9x^2
▲		y = 5 + 9 x  −x3/3 local minima 5+9x-x^3/3
▲		y = x3/3 − 9 x  − 7 local minima x^3/3-9x-7
▲		y = −x/(x2 + 1) local minima -x/(x^2+1)
▲		y = −(x2 + 1)/x local minima -(x^2+1)/x
▲		y = 25/x + x + 25 local minima 25/x+x+25
▲		y = (x2 − 6 x + 11 )1/2 local minima sqrt(x^2-6x+11)
▲		y = (x + 3)2·(x + 5) − 1 local minima (x+3)^2(x+5)-1
▲		y = x3/2 − 3 x + 1 local minima x^(3/2)-3x+1
▲		y = (2/3)·x3/2 − 2 x + 1 local minima (2/3)x^(3/2)-2x+1
▲		y =  x·x1/2 − 3 x + 1 local minima x*x^(1/2)-3x+1
▲		y = (2/3)·x·x1/2 − 2 x + 1 local minima (2/3)x*(x^(1/2))-2x+1
▲		y =7x^2 + 2x + 3 local minima 7^(x^2+2x-3)
▲		y = (x + 16) ex − 16 local minima (x+16)*E^(x-16)
▲		y = ( 3 −x ) e3 − x local minima (3-x)*E^(5-x)
▲		y = ( 3 x2 − 36 x + 36) ex − 36 local minima (3x^2-36x+36)*E^(x-36)
▲		y = ( x2 − 8 x + 8) e6 − x local minima (x^2-8x+8)*E^(6-x)
▲		y = ( x − 2 )2 ex − 5 local minima (x-2)^2*E^(x-5)
▲		y = ( x + 3 )2 e2 − x local minima (x+3)^2*E^(2-x)
▲		y = log5(x2 − 6 x + 12) + 2 local minima log(5,x^2-6 x+12)+2
▲		y =  2 x − ln ( x + 3 ) + 7 local minima 2x-ln(x+3)+7
▲		y = 3 x − ln (x + 3)3 local minima 3x-ln((x+3)^3)
▲		y = 2 x2 − 5 x + ln x − 3 local minima lnx+2x^2-5x-3
▲		y = (0.5 − x)·cos x + sin x из (0;0.5π) local minima (1/2-x)cosx+sinx for x=0..Pi/2
		ТОЧКА МАКСИМУМА Найдите точку максимума функции
▲		y = x3 − 48 x + 17 local maxima x^3-48x+17
▲		y = x3 − 3 x2 + 2 local maxima x^3-3x^2+2
▲		y = x3 + 2 x2 + x + 3 local maxima x^3+2x^2+x+3
▲		y = x3 − 5 x2 + 7 x − 5 local maxima x^3-5x^2+7x-5
▲		y = 7 + 12 x −x3 local maxima 7+12x-x^3
▲		y = 9 x2 −x3 local maxima 9x^2-x^3
▲		y = x3/3 − 9 x  − 7 local maxima (1/3)x^3-9x-7
▲		y = 5 + 9 x  −x3/3 local maxima 5+9x-(1/3)*x^3
▲		y = (x − 2)2·(x − 4) + 5 local maxima (x-2)^2*(x-4)+5
▲		y = −(x2 + 289)/x local maxima -(x^2+289)/x
▲		y = 16/x + x + 3 local maxima 16/x+x+3
▲		y = −x/(x2 + 289) local maxima -x/(x^2+289)
▲		y = 7 + 6 x − 2·x3/2 local maxima 7+6x-2x^(3/2)
▲		y = (4 − 4 x −x2)1/2 local maxima sqrt(4-4x-x^2)
▲		y =  −(2/3)·x3/2 + 3 x + 1 local maxima -(2/3)x^(3/2)+3x+1
▲		y = 7 + 6 x − 2 x·x1/2 local maxima 7+6x-2xsqrtx
▲		y = −(2/3)·x·x1/2 + 3 x + 1 local maxima -(2/3)sqrt(x^3)+3x+1
▲		y =116 x − x^2 local maxima 11^(6x-x^2)
▲		y = ( 9 −x ) ex + 9 local maxima (9-x)*E^(x+9)
▲		y = ( x + 16 ) e16 − x local maxima (x+16)*E^(16-x)
▲		y = ( 3 x2 − 36 x + 36) ex + 36 local maxima (3x^2-36x+36)*E^(x-36)
▲		y = ( x2 − 10 x + 10)  e5 − x local maxima (x^2-10x+10)*E^(5-x)
▲		y = ( x − 2 )2 ex − 6 local maxima (x-2)^2*E^(x-6)
▲		y = ( x + 6 )2 e4 − x local maxima (x+6)^2*E^(4-x)
▲		y =   ln ( x + 5 ) − 2 x + 9 local maxima ln(x+5)-2x+9
▲		y =  ln (x + 5)5 − 5 x local maxima ln((x+5)^5)-5x
▲		y =4 x − 4 ln (x + 7)  + 6 local maxima 4*x − 4*ln(x+7)+6
▲		y = 8 ln (x + 7) − 8 x + 3 local maxima 8ln(x+7)-8x+3
▲		y = 2 x2 − 13 x + 9 ln x + 8 local maxima 2x^2-13x+9lnx+8
▲		y = log2(2 +2 x −x2)−2 local maxima log(2,2+2x-x^2)-2
▲		y = (2 x  − 3)·cos x − 2 sin x + 5 из (0;π/2) local maxima (2 x-3) cosx-2 sinx+5 over (0,Pi/2)
		НАИМЕНЬШЕЕ ЗНАЧЕНИЕ Найдите наименьшее значение функцииу = f (x) на отрезке [a;b]
▲		y = x3− 27 x  →[0;4] minimize x^3-27x over [0,4]
▲		y = x3 − 3 x2 + 2 → [1;4] minimize x^3-3x^2+2 over [1,4]
▲		y = x3 − 2 x2 + x + 3→ [1;4] minimize x^3-2x^2+x+3 over [1,4]
▲		y = x3 −x2 − 40 x + 3  → [0;4] minimize x^3-x^2-40x+3 over [0,4]
▲		y = 7 + 12 x −x3 →  [-2;2] minimize 7+12x-x^3 over [-2,2]
▲		y = 9 x2 −x3 →  [-1;5] minimize 9x^2-x^3 over [-1,6]
▲		y = x3/3 − 9 x  − 7→  [-3;3] minimize (1/3)x^3-9x-7 over [-3,3]
▲		y = (x + 3)2·(x + 5) − 1  → [-4;-1] minimize (x+3)^2(x+5)-1 over [-4,1]
▲		y = (x2 + 25)/x  → [-10;-1] minimize (x^2+25)/x over [-10,-1]
▲		y =  x + 36/x  → [1;9] minimize x+36/x over [1,9]
▲		y = (x2 − 6 x + 13 )1/2 minimize sqrt(x^2-6x+13)
▲		y =  x·x1/2 − 3 x + 1 → [1;9] minimize x*x^(1/2) − 3*x + 1 over [1,9]
▲		y = (2/3)·x·x1/2 − 3 x + 1 → [1;9] minimize (2/3)x*x^(1/2)-3x+1 over [1,9]
▲		y = x3/2 − 3 x + 1 → [1;9] minimize x^(3/2)-3*x+1 over [1,9]
▲		y = (2/3)·x3/2 − 3 x + 1  → [1;9] minimize (2/3)*x^(3/2) − 3*x + 1 over [1,9]
▲		y =2x^2 + 2x + 5 minimize 2^(x^2+2x+5)
▲		y = (x − 8) ex − 7  → [6;8] minimize (x-8)*E^(x-7) over [6,8]
▲		y = (8 − x) e9 − x  → [3;10] minimize (8-x)*E^(9-x) over [3,10]
▲		y = (3 x2 − 36 x + 36) e x − 10  → [8;11] minimize (3x^2-36x+36)*E^(x-10) over [8,11]
▲		y = (x2 − 8 x + 8) e2 − x  →  [1;7] minimize (x^2-8x+8)*E^(2-x) over [1,7]
▲		y = (x − 2)2 e x − 2 →  [1;4] minimize (x-2)^2*E^(x-2) over [1,4]
▲		y = (x + 3)2 e −3 − x → [-5;-1] minimize (x+3)^2*E^(-3-x) over [-5,-1]
▲		y =e2x  − 6e2x  + 3→ [1;2] minimize E^(2*x)-6*E^x+3 over [1,2]
▲		y =  9 x − ln ( 9 x ) + 3    →  [1/18;5/18] minimize 9x-ln(9x)+3 over [-1/18,5/18]
▲		y =  2 x2 − 5 x  + ln x − 3  →  [5/6;7/6] minimize 2x^2-5x+lnx-3 over [5/6,7/6]
▲		y =  3 x − ln ( x + 3 )3    →  [−2.5;0] minimize 3x-ln((x+3)^3) over [-5/2,0]
▲		y =  4 x − 4 ln ( x + 7 ) + 6    →  [−6.5;0]  minimize 4x-4ln(x+7)+6 over [-13/2,0]
▲		y = log3(x2 − 6 x + 10) + 2 minimize log(3,x^2-6x+10)+2
▲		y = 7 sin x  − 8 x + 9  → [−1.5π;0] minimize 7sinx-8x+9 over [-3Pi/2,0]
▲		y =  5 sin x + (24/π)·x + 6 →  [−5π/6;0] minimize 5sinx+24x/Pi+6 over [-5Pi/6,0]
▲		y =  13 x − 9 sin x + 9 → [0;0.5π] minimize 13x-9sinx+9 over [0,Pi/2]
▲		y = 3 − 5 π/4 + 5 x − 5·21/2·sin x  → [0;0.5π] minimize 3-5Pi/4+5x-5sqrt2sinx over [0,Pi/2]
▲		y =  5 cos x − 6 x + 4 → [−1.5π;0]  minimize 5cosx-6x+4 over [-3Pi/2,0]
▲		y =  6 cos x + (24/π)·x + 5 → [−2π/3;0] minimize 6cosx+24x/Pi+5 over [-2Pi/3,0]
▲		y =  9 cos x + 14 x + 7 → [0;1.5π] minimize 9cosx+14x+7 over [0,3Pi/2]
▲		y = 3 + 5 π/4 − 5 x − 5·21/2·cosx→ [0;0.5π] minimize 3+5Pi/4-5x-5sqrt2*cosx over [0,Pi/2]
▲		y =  5 tg x − 5 x + 6  → [0;π/4] minimize 5tgx-5x+6 over [0,Pi/4]
▲		y =  4 tg x − 4 x − π + 5  →  [−π/4;π/4] minimize 4tgx-4x-Pi+5 over [-Pi/4,Pi/4]
▲		y =  4 x − 4 tg x + 12  → [−π/4;0] minimize 4x-4tgx+12 over [-Pi/4,0]
▲		y =  2 tg x − 4 x + π − 3 → [−π/3;π/3] minimize 2tgx-4x+Pi-3 over [-Pi/3,Pi/3]
▲		y = −14 x + 7 tg x + 35 π + 11 → [−π/3;π/3] minimize -14x+7tanx+7Pi/2+11 over [-Pi/3,Pi/3]
		НАИБОЛЬШЕЕ ЗНАЧЕНИЕ Найдите наибольшее значение функцииу = f (x) на отрезке [a;b]
▲		y = x3 − 3 x + 4  → [-2;0] maximize x^3-3x+4 over [-2,0]
▲		y = x3 − 6 x2  → [-3;3] maximize x^3-6x^2 over [-3,3]
▲		y = x3 + 2 x2 + x + 3→ [-4;-1] maximize x^3+2x^2+x+3 over [-4,-1]
▲		y = x3 + 2 x2 − 4 x + 4 → [-2;0] maximize x^3+2x^2-4x+4 over [-2,0]
▲		y = x3/3 − 9 x  − 7→ [-3;3] maximize (1/3)x^3-9x-7 over [-3,3]
▲		y = 7 + 12 x −x3 →  [-2;2] maximize 7+12x-x^3 over [-2,2]
▲		y = 9 x2 −x3 →  [2;10] maximize 9x^2-x^3 over [2,10]
▲		y = 5 + 9 x  −x3/3 → [-3;3] maximize 5+9x-(1/3)x^3 over [-3,3]
▲		y = (x − 2)2·(x − 4) + 5 → [1;3] maximize (x-2)^2*(x-4)+5 over [1,3]
▲		y = x5 − 5 x3 − 20 x→  [−6;1] maximize x^5-5*x^3-20*x over [-6,1]
▲		y = 3 x5 −20 x3 −54 x→  [−4;−1] maximize 3*x^5-20*x^3-54 over [-4,-1]
▲		y = (x2 + 25)/x → [1;10] maximize (x^2+25)/x over [1,10]
▲		y =  x + 9/x   → [-4;-1] maximize x+9/x over [-4,-1]
▲		y = (5 − 4 x −x2 )1/2 maximize sqrt(5-4x-x^2)
▲		y = 3 x − 2·x3/2 → [0;4] maximize 3x-2x^(3/2) over [0,4]
▲		y =  −(2/3)·x3/2 + 3 x + 1  → [1;9] maximize -(2/3)x^(3/2)+3x+1 over [1,9]
▲		y = 3 x − 2 x·x1/2  → [0;4] maximize 3x-2xsqrtx over [0,4]
▲		y =  −(2/3)·x x1/2 + 3 x + 1  → [1;9] maximize -(2/3)x*x^(1/2)+3x+1 over [1,9]
▲		y =3−7 − 6x − x^2 maximize 3^(-7-6x-x^2)
▲		y = (8 − x) e x − 7  →  [3;10] maximize (8-x)*E^(x-7) over [3,10]
▲		y = (x − 9) e10 − x  →  [-11;11] maximize (x-9)*E^(10-x) over [-11,11]
▲		y = (3 x2 − 36 x + 36) e x  →  [-1;4] maximize (3x^2-36x+36)*E^x over [-1,4]
▲		y = (x2 − 10 x + 10) e10 − x  →  [5;11] maximize (x^2-10x+10)*E^(10-x) over [5,11]
▲		y = (x − 2)2 e x  →  [-5;1] maximize (x-2)^2*E^x over [-5,1]
▲		y = (x + 6)2 e −4 − x → [-6;-1] maximize (x+6)^2*E^(-4-x) over [-6,-1]
▲		y =   ln ( x + 5 )5 − 5 x  →  [−45;0] maximize ln((x+5)^5)-5x over[-9/2,0]
▲		y =  8 ln ( x + 7 ) − 8 x + 3  →  [−65;0] maximize 8ln(x+7)-8x+3 over[-13/2,0]
▲		y =   ln ( 11 x ) − 11 x +9  →  [1/22;5/22] maximize ln(11x)-11x+9 over[1/22,5/22]
▲		y =  2 x2 − 13 x  + 9 ln x + 8 →  [13/14;15/14] maximize 2x^2-13x+9lnx+8 over[13/14,15/14]
▲		y = log5(4 − 2 x −x2) + 3 maximize log(5,4-2x-x^2)+3
▲		y =  10 sin x − (36/π)·x + 7 →  [−5π/6;0] maximize 10sinx-36x/Pi+7 over [-5Pi/6,0]
▲		y = 5 sin x − 6 x + 3   → [0;π/2] maximize 5sinx-6x+3 over [0,Pi/2]
▲		y = 12 sin x − 6·31/2·x + 31/2·π + 6  → [0;05π] maximize 12sinx-6sqrt3*x+sqrt3*Pi+6 over [0,Pi/2]
▲		y = 15 x − 3 sin x + 5 → [−05π;0] maximize 15x-3sinx+5 over [-Pi/2,0]
▲		y =  2 cos x − (18/π)·x + 4 →  [−2π/3;0] maximize 2cosx-18x/Pi+4 over [-2Pi/3,0]
▲		y = 12 cos x + 6·31/2·x − 2·31/2·π + 6   → [0;05π] maximize 12cosx+6sqrt3*x-2sqrt3*Pi+6 over [0,Pi/2]
▲		y =  7 cos x + 16 x − 2  → [−3π/2;0]  maximize 7cosx+16x-2 over [-3Pi/2,0]
▲		y = 4 cos x − 20 x + 7 → [0;3π/2] maximize 4cosx-20x+7 over [0,3Pi/2]
▲		y =  3 tg x − 3 x + 5  → [−025π;0] maximize 3tgx-3x+5 over [-Pi/4,0]
▲		y =  16 tg x − 16 x + 4π − 5 →  [−π/4;π/4]  maximize 16tan(x)-16x+4Pi-5 over [-Pi/4,Pi/4]
▲		y =  3 x − 3 tg x − 5 → [0;π/4] maximize 3x-3tgx-5 over [0,Pi/4]
▲		y =  14 x − 7 tg x − 35 π+ 11 → [−π/3;π/3] maximize 14x-7tgx-(7/2)Pi+11 over [-Pi/3,Pi/3]
▲		y = − 2 tg x + 4 x − π − 3→ [−π/3;π/3] maximize -2tgx+4x-Pi-3 over [-Pi/3,Pi/3]