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Popular Functions >

extreme f(x)=x^4-x^5

Solution

extreme points

f (x) = x^{4} - x^{5}

Solution

Minimum (0, 0), Maximum (\frac{4}{5}, \frac{256}{3125})

Solution steps

f^{'} (x) = 4 x^{3} - 5 x^{4}

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{4}{5},

Decreasing

: \frac{4}{5} < x < \infty

Plug

x = 0

into

x^{4} - x^{5} : 0

Minimum (0, 0)

Plug

x = \frac{4}{5}

into

x^{4} - x^{5} : \frac{256}{3125}

Maximum (\frac{4}{5}, \frac{256}{3125})

Minimum (0, 0), Maximum (\frac{4}{5}, \frac{256}{3125})

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=x^4-x^5 ?
The extreme f(x)=x^4-x^5 is Minimum(0,0),Maximum(4/5 , 256/3125)