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

The extreme f(x)=-x^3-x^2 is Minimum(-2/3 ,-4/27),Maximum(0,0)

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

extreme points

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

Minimum (- \frac{2}{3}, - \frac{4}{27}), Maximum (0, 0)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - \frac{2}{3},

Increasing

: - \frac{2}{3} < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - \frac{2}{3}

into

- x^{3} - x^{2} : - \frac{4}{27}

Minimum (- \frac{2}{3}, - \frac{4}{27})

Plug

x = 0

into

- x^{3} - x^{2} : 0

Maximum (0, 0)

Minimum (- \frac{2}{3}, - \frac{4}{27}), Maximum (0, 0)

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

f (x) = - x^{\frac{2}{3}} (x - 5)

\frac{x ^{2} - 7 x + 26}{x - 5}

f (x) = 3 x^{3} e^{- x}, - 1 \leq x \leq 5

(x + 8)^{\frac{2}{3}}

What is the extreme f(x)=-x^3-x^2 ?
The extreme f(x)=-x^3-x^2 is Minimum(-2/3 ,-4/27),Maximum(0,0)