What is the extreme f(x)=-5x^3+45x ?

The extreme f(x)=-5x^3+45x is Minimum(-sqrt(3),-30sqrt(3)),Maximum(sqrt(3),30sqrt(3))

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extreme f(x)=-5x^3+45x

extreme

Minimum (- 3, - 303), Maximum (3, 303)

Solution steps

f^{'} (x) = - 15 x^{2} + 45

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 3

into

- 5 x^{3} + 45 x : - 303

Minimum (- 3, - 303)

Plug

x = 3

into

- 5 x^{3} + 45 x : 303

Maximum (3, 303)

Minimum (- 3, - 303), Maximum (3, 303)

What is the extreme f(x)=-5x^3+45x ?
The extreme f(x)=-5x^3+45x is Minimum(-sqrt(3),-30sqrt(3)),Maximum(sqrt(3),30sqrt(3))