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Popular Functions >

extreme x^4-x^5

Solution

extreme points

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

Popular Examples

extreme f(x)=3x^4+4x^3-120x^2+120

extreme f(x)=14x^2-7x^4

extreme f(x)=30x^4-13x^3-54x^2-1

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

extreme f(x)=8-x,-1<= x<= 3

Frequently Asked Questions (FAQ)

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