What is the extreme f(x)=-x^3+9x^2+120x-200,x>= 5 ?

The extreme f(x)=-x^3+9x^2+120x-200,x>= 5 is Minimum(5,500),Maximum(10,900)

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extreme f(x)=-x^3+9x^2+120x-200,x>= 5

extreme

Minimum (5, 500), Maximum (10, 900)

Solution steps

Find the critical points:

x = 5, x = 10

Domain of

- x^{3} + 9 x^{2} + 120 x - 200, x \geq 5 : x \geq 5

Find intervals:

Increasing

: 5 < x < 10,

Decreasing

: 10 < x < \infty

Plug the extreme point

x = 5

into

- x^{3} + 9 x^{2} + 120 x - 200 \Rightarrow y = 500

Minimum (5, 500)

Plug the extreme point

x = 10

into

- x^{3} + 9 x^{2} + 120 x - 200 \Rightarrow y = 900

Maximum (10, 900)

Minimum (5, 500), Maximum (10, 900)

What is the extreme f(x)=-x^3+9x^2+120x-200,x>= 5 ?
The extreme f(x)=-x^3+9x^2+120x-200,x>= 5 is Minimum(5,500),Maximum(10,900)