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

The extreme f(x)=x^3+15x^2 is Maximum(-10,500),Minimum(0,0)

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

extreme points

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

Maximum (- 10, 500), Minimum (0, 0)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 10,

Decreasing

: - 10 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 10

into

x^{3} + 15 x^{2} : 500

Maximum (- 10, 500)

Plug

x = 0

into

x^{3} + 15 x^{2} : 0

Minimum (0, 0)

Maximum (- 10, 500), Minimum (0, 0)

What is the extreme f(x)=x^3+15x^2 ?
The extreme f(x)=x^3+15x^2 is Maximum(-10,500),Minimum(0,0)