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Popular >

extreme f(x)=x^3-x^4

Solution

extreme points

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

Solution

Saddle (0, 0), Maximum (\frac{3}{4}, \frac{27}{256})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{3}{4},

Decreasing

: \frac{3}{4} < x < \infty

Plug

x = 0

into

x^{3} - x^{4} : 0

Saddle (0, 0)

Plug

x = \frac{3}{4}

into

x^{3} - x^{4} : \frac{27}{256}

Maximum (\frac{3}{4}, \frac{27}{256})

Saddle (0, 0), Maximum (\frac{3}{4}, \frac{27}{256})

Popular Examples

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f (x, y) = x^{3} - 3 x y

extreme f(x)=(x-1)^3+2 extreme points

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

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f (y, z) = ln (1 + y^{2} + z^{2})

extreme 3x^3-9x extreme points

3 x^{3} - 9 x

Frequently Asked Questions (FAQ)

What is the extreme f(x)=x^3-x^4 ?
The extreme f(x)=x^3-x^4 is Saddle(0,0),Maximum(3/4 , 27/256)