What is the extreme f(x)= 1/5 x^5-1/2 x^4 ?

The extreme f(x)= 1/5 x^5-1/2 x^4 is Maximum(0,0),Minimum(2,-8/5)

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extreme f(x)= 1/5 x^5-1/2 x^4

extreme points

f (x) = \frac{1}{5} x^{5} - \frac{1}{2} x^{4}

Maximum (0, 0), Minimum (2, - \frac{8}{5})

Solution steps

f^{'} (x) = x^{4} - 2 x^{3}

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = 0

into

\frac{1}{5} x^{5} - \frac{1}{2} x^{4} : 0

Maximum (0, 0)

Plug

x = 2

into

\frac{1}{5} x^{5} - \frac{1}{2} x^{4} : - \frac{8}{5}

Minimum (2, - \frac{8}{5})

Maximum (0, 0), Minimum (2, - \frac{8}{5})

f (x) = 3 - x, 1 \leq x \leq 3

f (x) = x^{3} e^{(4 - 2 x^{2})}

x^{2} - x y + y^{2} + 9 x - 6 y + 10

f (x) = 39 x^{\frac{27}{13}} - 81 x

x y^{2} + x^{3} y - x y

What is the extreme f(x)= 1/5 x^5-1/2 x^4 ?
The extreme f(x)= 1/5 x^5-1/2 x^4 is Maximum(0,0),Minimum(2,-8/5)