en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=x^7-x^5

Solution

extreme points

f (x) = x^{7} - x^{5}

Solution

Maximum (- \frac{5}{7}, - (\frac{5}{7})^{\frac{7}{2}} + (\frac{5}{7})^{\frac{5}{2}}), Saddle (0, 0), Minimum (\frac{5}{7}, (\frac{5}{7})^{\frac{7}{2}} - (\frac{5}{7})^{\frac{5}{2}})

Solution steps

f^{'} (x) = 7 x^{6} - 5 x^{4}

Find intervals:

Increasing

: - \infty < x < - \frac{5}{7},

Decreasing

: - \frac{5}{7} < x < 0,

Decreasing

: 0 < x < \frac{5}{7},

Increasing

: \frac{5}{7} < x < \infty

Plug

x = - \frac{5}{7}

into

x^{7} - x^{5} : - (\frac{5}{7})^{\frac{7}{2}} + (\frac{5}{7})^{\frac{5}{2}}

Maximum (- \frac{5}{7}, - (\frac{5}{7})^{\frac{7}{2}} + (\frac{5}{7})^{\frac{5}{2}})

Plug

x = 0

into

x^{7} - x^{5} : 0

Saddle (0, 0)

Plug

x = \frac{5}{7}

into

x^{7} - x^{5} : (\frac{5}{7})^{\frac{7}{2}} - (\frac{5}{7})^{\frac{5}{2}}

Minimum (\frac{5}{7}, (\frac{5}{7})^{\frac{7}{2}} - (\frac{5}{7})^{\frac{5}{2}})

Maximum (- \frac{5}{7}, - (\frac{5}{7})^{\frac{7}{2}} + (\frac{5}{7})^{\frac{5}{2}}), Saddle (0, 0), Minimum (\frac{5}{7}, (\frac{5}{7})^{\frac{7}{2}} - (\frac{5}{7})^{\frac{5}{2}})

Graph

Popular Examples

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

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

extreme xsqrt(x-1)extreme points

x x - 1

extreme f(x)=x^3-15x^2+12x+7 extreme points

f (x) = x^{3} - 15 x^{2} + 12 x + 7

extreme f(x)=3x^2-4x extreme points

f (x) = 3 x^{2} - 4 x

extreme f(x,y)=sqrt(x^2+y^2+16)extreme points

f (x, y) = x^{2} + y^{2} + 16

Frequently Asked Questions (FAQ)

What is the extreme f(x)=x^7-x^5 ?
The extreme f(x)=x^7-x^5 is