What is the extreme f(x)=(x-2)(x-5)^3+11 ?

The extreme f(x)=(x-2)(x-5)^3+11 is Minimum(11/4 , 629/256),Saddle(5,11)

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extreme f(x)=(x-2)(x-5)^3+11

extreme points

f (x) = (x - 2) (x - 5)^{3} + 11

Minimum (\frac{11}{4}, \frac{629}{256}), Saddle (5, 11)

Solution steps

f^{'} (x) = 4 x^{3} - 51 x^{2} + 210 x - 275

Find intervals:

Decreasing

: - \infty < x < \frac{11}{4},

Increasing

: \frac{11}{4} < x < 5,

Increasing

: 5 < x < \infty

Plug

x = \frac{11}{4}

into

(x - 2) (x - 5)^{3} + 11 : \frac{629}{256}

Minimum (\frac{11}{4}, \frac{629}{256})

Plug

x = 5

into

(x - 2) (x - 5)^{3} + 11 : 11

Saddle (5, 11)

Minimum (\frac{11}{4}, \frac{629}{256}), Saddle (5, 11)

What is the extreme f(x)=(x-2)(x-5)^3+11 ?
The extreme f(x)=(x-2)(x-5)^3+11 is Minimum(11/4 , 629/256),Saddle(5,11)