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)

f (x, y) = 3 x^{4} - 2 x y^{2} + 4 y^{3} + 1

f (x) = \frac{1}{3} x^{3} - x

f (x, y) = - 3 x^{2} - 2 x y - 2 y^{2} + 400 x + 200 y

f (x, y) = 2 - 5 x^{2} - 2 y^{2}

f (x, y) = ln (9 - x^{2} - y^{2})

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)