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Popular >

extreme 3x^4-4x^3

Solution

extreme points

3 x^{4} - 4 x^{3}

Solution

Saddle (0, 0), Minimum (1, - 1)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = 0

into

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

Saddle (0, 0)

Plug

x = 1

into

3 x^{4} - 4 x^{3} : - 1

Minimum (1, - 1)

Saddle (0, 0), Minimum (1, - 1)

Popular Examples

intercepts of ln(x)+2 intercepts

ln (x) + 2

monotone f(x)=(x^2)/(x^2-1)monotone intervals

f (x) = \frac{x ^{2}}{x ^{2} - 1}

domain of f(x)=x^2+2x-1 domain

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

domain of f(x)=(3x)/(x^2+3)domain

f (x) = \frac{3 x}{x ^{2} + 3}

domain of g(x)=(\sqrt[4]{x})^5 domain

Frequently Asked Questions (FAQ)

What is the extreme 3x^4-4x^3 ?
The extreme 3x^4-4x^3 is Saddle(0,0),Minimum(1,-1)