What is the extreme 1/3 x^3-1/2 x^2+1 ?

The extreme 1/3 x^3-1/2 x^2+1 is Maximum(0,1),Minimum(1, 5/6)

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extreme 1/3 x^3-1/2 x^2+1

extreme points

\frac{1}{3} x^{3} - \frac{1}{2} x^{2} + 1

Maximum (0, 1), Minimum (1, \frac{5}{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} + 1 : 1

Maximum (0, 1)

Plug

x = 1

into

\frac{1}{3} x^{3} - \frac{1}{2} x^{2} + 1 : \frac{5}{6}

Minimum (1, \frac{5}{6})

Maximum (0, 1), Minimum (1, \frac{5}{6})

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

f (x, y) = x^{3} + y^{2} - 4 x y + 17 x - 10 y + 2021

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

y = 7 x + 7 sin (x)

f (x) = 4 x^{2} + 3 x^{2} - 6 x + 1

What is the extreme 1/3 x^3-1/2 x^2+1 ?
The extreme 1/3 x^3-1/2 x^2+1 is Maximum(0,1),Minimum(1, 5/6)