What is the extreme x^6(x-4)^5 ?

The extreme x^6(x-4)^5 is Maximum(0,0),Minimum(24/11 ,-(6.1153E14)/(11^{11)}),Saddle(4,0)

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extreme x^6(x-4)^5

extreme points

x^{6} (x - 4)^{5}

Maximum (0, 0), Minimum (\frac{24}{11}, - \frac{6.1153 E 14}{1 1 ^{11}}), Saddle (4, 0)

Solution steps

f^{'} (x) = x^{5} (x - 4)^{4} (11 x - 24)

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{24}{11},

Increasing

: \frac{24}{11} < x < 4,

Increasing

: 4 < x < \infty

Plug

x = 0

into

x^{6} (x - 4)^{5} : 0

Maximum (0, 0)

Plug

x = \frac{24}{11}

into

x^{6} (x - 4)^{5} : - \frac{6.1153 E 14}{1 1 ^{11}}

Minimum (\frac{24}{11}, - \frac{6.1153 E 14}{1 1 ^{11}})

Plug

x = 4

into

x^{6} (x - 4)^{5} : 0

Saddle (4, 0)

Maximum (0, 0), Minimum (\frac{24}{11}, - \frac{6.1153 E 14}{1 1 ^{11}}), Saddle (4, 0)

2 x^{2} + 3

f (x) = 2 x^{3} - 6 x^{2}

f (x) = x^{2} - 8 x + 20

π r^{2} + x^{2}

\frac{( x - 1 )}{( x + 1 ) ^{2}}

What is the extreme x^6(x-4)^5 ?
The extreme x^6(x-4)^5 is Maximum(0,0),Minimum(24/11 ,-(6.1153E14)/(11^{11)}),Saddle(4,0)