What is the extreme f(x)=x^8(x-3)^7 ?

The extreme f(x)=x^8(x-3)^7 is Maximum(0,0),Minimum(8/5 ,-(1.38168E13)/(5^{15)}),Saddle(3,0)

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extreme f(x)=x^8(x-3)^7

extreme

Maximum (0, 0), Minimum (\frac{8}{5}, - \frac{1.38168 E 13}{5 ^{15}}), Saddle (3, 0)

Solution steps

f^{'} (x) = 3 x^{7} (x - 3)^{6} (5 x - 8)

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{8}{5},

Increasing

: \frac{8}{5} < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 0

into

x^{8} (x - 3)^{7} : 0

Maximum (0, 0)

Plug

x = \frac{8}{5}

into

x^{8} (x - 3)^{7} : - \frac{1.38168 E 13}{5 ^{15}}

Minimum (\frac{8}{5}, - \frac{1.38168 E 13}{5 ^{15}})

Plug

x = 3

into

x^{8} (x - 3)^{7} : 0

Saddle (3, 0)

Maximum (0, 0), Minimum (\frac{8}{5}, - \frac{1.38168 E 13}{5 ^{15}}), Saddle (3, 0)

What is the extreme f(x)=x^8(x-3)^7 ?
The extreme f(x)=x^8(x-3)^7 is Maximum(0,0),Minimum(8/5 ,-(1.38168E13)/(5^{15)}),Saddle(3,0)