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Popular >

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})

Popular Examples

extreme-2e^{-2x}(x^4-2x^3)extreme points

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

extreme f(x)=x^4+6x^3-5x^2+2x+3 extreme points

f (x) = x^{4} + 6 x^{3} - 5 x^{2} + 2 x + 3

extreme f(x)=x^2-8x+17 extreme points

f (x) = x^{2} - 8 x + 17

extreme f(x)=8x^2-x^4 extreme points

f (x) = 8 x^{2} - x^{4}

extreme f(t)=r(t)e^{-at}extreme points

f (t) = r (t) e^{- a t}

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)