en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Functions >

extreme t-\sqrt[3]{t}

Solution

extreme

Solution

Maximum (- \frac{1}{3 3}, - \frac{1}{3 3} + 3 \frac{1}{3 3}), Minimum (\frac{1}{3 3}, \frac{1}{3 3} - 3 \frac{1}{3 3})

Solution steps

f^{'} (t) = 1 - \frac{1}{3 t ^{\frac{2}{3}}}

Find intervals:

Increasing

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

Decreasing

: - \frac{1}{3 3} < t < 0,

Decreasing

: 0 < t < \frac{1}{3 3},

Increasing

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

Plug

t = - \frac{1}{3 3}

into

t - 3 t : - \frac{1}{3 3} + 3 \frac{1}{3 3}

Maximum (- \frac{1}{3 3}, - \frac{1}{3 3} + 3 \frac{1}{3 3})

Plug

t = \frac{1}{3 3}

into

t - 3 t : \frac{1}{3 3} - 3 \frac{1}{3 3}

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

Maximum (- \frac{1}{3 3}, - \frac{1}{3 3} + 3 \frac{1}{3 3}), Minimum (\frac{1}{3 3}, \frac{1}{3 3} - 3 \frac{1}{3 3})

Graph

Popular Examples

extreme f(x)=7xsqrt(x-x^2)

extreme f(x)=3x^4-12x^3

extreme f(x)=x^3-x^2-12+2,0<= x<= 4

extreme f(x)=(x^2)/(x^2+108)

extreme f(x)=4x+5

Frequently Asked Questions (FAQ)

What is the extreme t-\sqrt[3]{t} ?
The extreme t-\sqrt[3]{t} is