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Popular Functions >

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

Solution

extreme points

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

Solution

Maximum (- \frac{1}{2}, 1), Minimum (\frac{1}{2}, - 1)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - \frac{1}{2},

Decreasing

: - \frac{1}{2} < x < \frac{1}{2},

Increasing

: \frac{1}{2} < x < \infty

Plug

x = - \frac{1}{2}

into

4 x^{3} - 3 x : 1

Maximum (- \frac{1}{2}, 1)

Plug

x = \frac{1}{2}

into

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

Minimum (\frac{1}{2}, - 1)

Maximum (- \frac{1}{2}, 1), Minimum (\frac{1}{2}, - 1)

Graph

Popular Examples

extreme f(x,y)=x^3+y^3+4xy

extreme f(x)=6x^5-40x^3+45

extreme f(x)=x^3-3x,-2<= x<= 2

extreme f(x,y)=13xe^y

extreme y=-x^2+4

Frequently Asked Questions (FAQ)

What is the extreme f(x)=4x^3-3x ?
The extreme f(x)=4x^3-3x is Maximum(-1/2 ,1),Minimum(1/2 ,-1)