What is the extreme f(x)=-x^3+6x^2+63x ?

The extreme f(x)=-x^3+6x^2+63x is Minimum(-3,-108),Maximum(7,392)

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extreme f(x)=-x^3+6x^2+63x

extreme points

f (x) = - x^{3} + 6 x^{2} + 63 x

Minimum (- 3, - 108), Maximum (7, 392)

Solution steps

f^{'} (x) = - 3 x^{2} + 12 x + 63

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 7,

Decreasing

: 7 < x < \infty

Plug

x = - 3

into

- x^{3} + 6 x^{2} + 63 x : - 108

Minimum (- 3, - 108)

Plug

x = 7

into

- x^{3} + 6 x^{2} + 63 x : 392

Maximum (7, 392)

Minimum (- 3, - 108), Maximum (7, 392)

What is the extreme f(x)=-x^3+6x^2+63x ?
The extreme f(x)=-x^3+6x^2+63x is Minimum(-3,-108),Maximum(7,392)