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Popular >

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

Solution

extreme points

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

Solution

Saddle (0, 0), Maximum (3, 27)

Solution steps

f^{'} (x) = 12 x^{2} - 4 x^{3}

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = 0

into

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

Saddle (0, 0)

Plug

x = 3

into

4 x^{3} - x^{4} : 27

Maximum (3, 27)

Saddle (0, 0), Maximum (3, 27)

Popular Examples

domain of sqrt((x^2)/(x^2-1))domain

\frac{x ^{2}}{x ^{2} - 1}

inverse of f(x)=(2x^2-7x+2)/(x-4)inverse

f (x) = \frac{2 x ^{2} - 7 x + 2}{x - 4}

extreme f(x)=x^{6/5}-12x^{1/5}extreme points

f (x) = x^{\frac{6}{5}} - 12 x^{\frac{1}{5}}

slope ofintercept-3x-2y=6 slope intercept

- 3 x - 2 y = 6

symmetry x^2+y-25=0 symmetry

x^{2} + y - 25 = 0

Frequently Asked Questions (FAQ)

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