What is the extreme f(x)=x^3-6x^2+5,-3<= x<= 5 ?

The extreme f(x)=x^3-6x^2+5,-3<= x<= 5 is Minimum(-3,-76),Maximum(0,5),Minimum(4,-27),Maximum(5,-20)

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extreme f(x)=x^3-6x^2+5,-3<= x<= 5

extreme points

f (x) = x^{3} - 6 x^{2} + 5, - 3 \leq x \leq 5

Minimum (- 3, - 76), Maximum (0, 5), Minimum (4, - 27), Maximum (5, - 20)

Solution steps

Find the critical points:

x = - 3, x = 0, x = 4, x = 5

Domain of

x^{3} - 6 x^{2} + 5, - 3 \leq x \leq 5 : - 3 \leq x \leq 5

Find intervals:

Increasing

: - 3 < x < 0,

Decreasing

: 0 < x < 4,

Increasing

: 4 < x < 5

Plug the extreme point

x = - 3

into

x^{3} - 6 x^{2} + 5 \Rightarrow y = - 76

Minimum (- 3, - 76)

Plug the extreme point

x = 0

into

x^{3} - 6 x^{2} + 5 \Rightarrow y = 5

Maximum (0, 5)

Plug the extreme point

x = 4

into

x^{3} - 6 x^{2} + 5 \Rightarrow y = - 27

Minimum (4, - 27)

Plug the extreme point

x = 5

into

x^{3} - 6 x^{2} + 5 \Rightarrow y = - 20

Maximum (5, - 20)

Minimum (- 3, - 76), Maximum (0, 5), Minimum (4, - 27), Maximum (5, - 20)

What is the extreme f(x)=x^3-6x^2+5,-3<= x<= 5 ?
The extreme f(x)=x^3-6x^2+5,-3<= x<= 5 is Minimum(-3,-76),Maximum(0,5),Minimum(4,-27),Maximum(5,-20)