What is the extreme f(x)=x^6-3x^5 ?

The extreme f(x)=x^6-3x^5 is Saddle(0,0),Minimum(5/2 ,-3125/64)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=x^6-3x^5

extreme points

f (x) = x^{6} - 3 x^{5}

Saddle (0, 0), Minimum (\frac{5}{2}, - \frac{3125}{64})

Solution steps

f^{'} (x) = 6 x^{5} - 15 x^{4}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{5}{2},

Increasing

: \frac{5}{2} < x < \infty

Plug

x = 0

into

x^{6} - 3 x^{5} : 0

Saddle (0, 0)

Plug

x = \frac{5}{2}

into

x^{6} - 3 x^{5} : - \frac{3125}{64}

Minimum (\frac{5}{2}, - \frac{3125}{64})

Saddle (0, 0), Minimum (\frac{5}{2}, - \frac{3125}{64})

What is the extreme f(x)=x^6-3x^5 ?
The extreme f(x)=x^6-3x^5 is Saddle(0,0),Minimum(5/2 ,-3125/64)