What is the extreme f(x)=-x^3-15x^2-3 ?

The extreme f(x)=-x^3-15x^2-3 is Minimum(-10,-503),Maximum(0,-3)

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extreme f(x)=-x^3-15x^2-3

extreme points

f (x) = - x^{3} - 15 x^{2} - 3

Minimum (- 10, - 503), Maximum (0, - 3)

Solution steps

f^{'} (x) = - 3 x^{2} - 30 x

Find intervals:

Decreasing

: - \infty < x < - 10,

Increasing

: - 10 < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - 10

into

- x^{3} - 15 x^{2} - 3 : - 503

Minimum (- 10, - 503)

Plug

x = 0

into

- x^{3} - 15 x^{2} - 3 : - 3

Maximum (0, - 3)

Minimum (- 10, - 503), Maximum (0, - 3)

What is the extreme f(x)=-x^3-15x^2-3 ?
The extreme f(x)=-x^3-15x^2-3 is Minimum(-10,-503),Maximum(0,-3)