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

The extreme f(x)= 1/3 x^3-1/2 x^2 is Maximum(0,0),Minimum(1,-1/6)

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

extreme points

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

Maximum (0, 0), Minimum (1, - \frac{1}{6})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = 0

into

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

Maximum (0, 0)

Plug

x = 1

into

\frac{1}{3} x^{3} - \frac{1}{2} x^{2} : - \frac{1}{6}

Minimum (1, - \frac{1}{6})

Maximum (0, 0), Minimum (1, - \frac{1}{6})

x x^{2} + 25

f (x, y) = 2 x^{2} + 3 x y + 4 y^{2} + 2 x - 10 y

\frac{1}{2 x + 3}

f (x, y) = \frac{- 2 y}{4 x ^{2} + y ^{2} + 2}

f (x) = x e^{- 6 x}, 0 \leq x \leq 2

What is the extreme f(x)= 1/3 x^3-1/2 x^2 ?
The extreme f(x)= 1/3 x^3-1/2 x^2 is Maximum(0,0),Minimum(1,-1/6)