What is the extreme f(x)=x^3+9x^2 ?

The extreme f(x)=x^3+9x^2 is Maximum(-6,108),Minimum(0,0)

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extreme f(x)=x^3+9x^2

extreme points

f (x) = x^{3} + 9 x^{2}

Maximum (- 6, 108), Minimum (0, 0)

Solution steps

f^{'} (x) = 3 x^{2} + 18 x

Find intervals:

Increasing

: - \infty < x < - 6,

Decreasing

: - 6 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 6

into

x^{3} + 9 x^{2} : 108

Maximum (- 6, 108)

Plug

x = 0

into

x^{3} + 9 x^{2} : 0

Minimum (0, 0)

Maximum (- 6, 108), Minimum (0, 0)

f (x) = - x^{2} + 7 x

f (x, y) = 2 ln (x) + ln (y) - 4 x - y

f (x, y) = e^{2 x^{2} + x y + y^{2}}

f (x) = \frac{x ^{3}}{x + 4}

f (x) = x^{2} + 6 x + 10

What is the extreme f(x)=x^3+9x^2 ?
The extreme f(x)=x^3+9x^2 is Maximum(-6,108),Minimum(0,0)