What is the extreme f(x)= 1/3 x^3+x^2 ?

The extreme f(x)= 1/3 x^3+x^2 is Maximum(-2, 4/3),Minimum(0,0)

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extreme f(x)= 1/3 x^3+x^2

extreme points

f (x) = \frac{1}{3} x^{3} + x^{2}

Maximum (- 2, \frac{4}{3}), Minimum (0, 0)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 2

into

\frac{1}{3} x^{3} + x^{2} : \frac{4}{3}

Maximum (- 2, \frac{4}{3})

Plug

x = 0

into

\frac{1}{3} x^{3} + x^{2} : 0

Minimum (0, 0)

Maximum (- 2, \frac{4}{3}), Minimum (0, 0)

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

f (x) = x (x - 1) (2 x - 1)

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

f (x) = \frac{1}{2} cot (π x)

3

What is the extreme f(x)= 1/3 x^3+x^2 ?
The extreme f(x)= 1/3 x^3+x^2 is Maximum(-2, 4/3),Minimum(0,0)