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Popular >

extreme 3x^3-x-3

Solution

extreme points

3 x^{3} - x - 3

Solution

Maximum (- \frac{1}{3}, - \frac{25}{9}), Minimum (\frac{1}{3}, - \frac{29}{9})

Solution steps

f^{'} (x) = 9 x^{2} - 1

Find intervals:

Increasing

: - \infty < x < - \frac{1}{3},

Decreasing

: - \frac{1}{3} < x < \frac{1}{3},

Increasing

: \frac{1}{3} < x < \infty

Plug

x = - \frac{1}{3}

into

3 x^{3} - x - 3 : - \frac{25}{9}

Maximum (- \frac{1}{3}, - \frac{25}{9})

Plug

x = \frac{1}{3}

into

3 x^{3} - x - 3 : - \frac{29}{9}

Minimum (\frac{1}{3}, - \frac{29}{9})

Maximum (- \frac{1}{3}, - \frac{25}{9}), Minimum (\frac{1}{3}, - \frac{29}{9})

Popular Examples

domain of f(x)=(sqrt(x+2))/(x-1)domain

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

domain of f(x)=sqrt(x^2)domain

f (x) = x^{2}

inverse of f(x)=ln(x-7)inverse

f (x) = ln (x - 7)

asymptotes of f(x)=(6x-15)/(x+2)asymptotes

f (x) = \frac{6 x - 15}{x + 2}

intercepts of h(t)=-490t^2+75t+12 intercepts

h (t) = - 490 t^{2} + 75 t + 12

Frequently Asked Questions (FAQ)

What is the extreme 3x^3-x-3 ?
The extreme 3x^3-x-3 is Maximum(-1/3 ,-25/9),Minimum(1/3 ,-29/9)