en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=t-t^{1/3}

Solution

extreme points

f (x) = t - t^{\frac{1}{3}}

Solution

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

Solution steps

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

Find intervals:

Increasing

: - \infty < t < - \frac{1}{3 \cdot 3 ^{\frac{1}{2}}},

Decreasing

: - \frac{1}{3 \cdot 3 ^{\frac{1}{2}}} < t < 0,

Decreasing

: 0 < t < \frac{1}{3 \cdot 3 ^{\frac{1}{2}}},

Increasing

: \frac{1}{3 \cdot 3 ^{\frac{1}{2}}} < t < \infty

Plug

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

into

t - t^{\frac{1}{3}} : - \frac{1}{3 3} + (\frac{1}{3 3})^{\frac{1}{3}}

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

Plug

t = \frac{1}{3 3}

into

t - t^{\frac{1}{3}} : \frac{1}{3 3} - (\frac{1}{3 3})^{\frac{1}{3}}

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

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

Graph

Popular Examples

extreme f(x,y)=x^2+y^2-2 extreme points

f (x, y) = x^{2} + y^{2} - 2

extreme f(x,y)=3x^3-2x^2y+5xy-y^3-1 extreme points

f (x, y) = 3 x^{3} - 2 x^{2} y + 5 x y - y^{3} - 1

extreme f(x)=(3-x)e^{x-3}extreme points

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

extreme f(x)=1+x^2e^{5-3x}extreme points

f (x) = 1 + x^{2} e^{5 - 3 x}

extreme y=-4e^{-4t}+5e^{-5t}extreme points

y = - 4 e^{- 4 t} + 5 e^{- 5 t}

Frequently Asked Questions (FAQ)

What is the extreme f(x)=t-t^{1/3} ?
The extreme f(x)=t-t^{1/3} is