What is the extreme f(x)=2x^3+9x^2-60x+7,-5<= x<= 5 ?

The extreme f(x)=2x^3+9x^2-60x+7,-5<= x<= 5 is Maximum(-5,282),Minimum(2,-61),Maximum(5,182)

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extreme f(x)=2x^3+9x^2-60x+7,-5<= x<= 5

extreme points

f (x) = 2 x^{3} + 9 x^{2} - 60 x + 7, - 5 \leq x \leq 5

Maximum (- 5, 282), Minimum (2, - 61), Maximum (5, 182)

Solution steps

Find the critical points:

x = - 5, x = 2, x = 5

Domain of

2 x^{3} + 9 x^{2} - 60 x + 7, - 5 \leq x \leq 5 : - 5 \leq x \leq 5

Find intervals:

Decreasing

: - 5 < x < 2,

Increasing

: 2 < x < 5

Plug the extreme point

x = - 5

into

2 x^{3} + 9 x^{2} - 60 x + 7 \Rightarrow y = 282

Maximum (- 5, 282)

Plug the extreme point

x = 2

into

2 x^{3} + 9 x^{2} - 60 x + 7 \Rightarrow y = - 61

Minimum (2, - 61)

Plug the extreme point

x = 5

into

2 x^{3} + 9 x^{2} - 60 x + 7 \Rightarrow y = 182

Maximum (5, 182)

Maximum (- 5, 282), Minimum (2, - 61), Maximum (5, 182)

f (x) = x^{3} + 4 x^{2} + 4 x

f (x) = (x + 2)^{2} (x - 3)^{3}

y = (x - 2)^{3} (x + 2)

f (x) = 100 - \frac{1}{4} (x^{2} + 33 x)

f (x, y) = - 2 x^{2} + 5 y^{2} - 9 x + 9 y + 6

What is the extreme f(x)=2x^3+9x^2-60x+7,-5<= x<= 5 ?
The extreme f(x)=2x^3+9x^2-60x+7,-5<= x<= 5 is Maximum(-5,282),Minimum(2,-61),Maximum(5,182)