What is the extreme x^6(x-1)^5 ?

The extreme x^6(x-1)^5 is Maximum(0,0),Minimum(6/11 ,-(145800000)/(11^{11)}),Saddle(1,0)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme x^6(x-1)^5

extreme points

x^{6} (x - 1)^{5}

Maximum (0, 0), Minimum (\frac{6}{11}, - \frac{145800000}{1 1 ^{11}}), Saddle (1, 0)

Solution steps

f^{'} (x) = x^{5} (x - 1)^{4} (11 x - 6)

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{6}{11},

Increasing

: \frac{6}{11} < x < 1,

Increasing

: 1 < x < \infty

Plug

x = 0

into

x^{6} (x - 1)^{5} : 0

Maximum (0, 0)

Plug

x = \frac{6}{11}

into

x^{6} (x - 1)^{5} : - \frac{145800000}{1 1 ^{11}}

Minimum (\frac{6}{11}, - \frac{145800000}{1 1 ^{11}})

Plug

x = 1

into

x^{6} (x - 1)^{5} : 0

Saddle (1, 0)

Maximum (0, 0), Minimum (\frac{6}{11}, - \frac{145800000}{1 1 ^{11}}), Saddle (1, 0)

f (x) = \frac{( 5 + x ^{4} )}{x ^{2} - x ^{4}}

f (x) = - sin (x - \frac{π}{3})

f (x) = \frac{5}{3 x - 9}

f (x) = 17

2 x - y = 6, (- 7, - 8)

What is the extreme x^6(x-1)^5 ?
The extreme x^6(x-1)^5 is Maximum(0,0),Minimum(6/11 ,-(145800000)/(11^{11)}),Saddle(1,0)