What is the extreme (5-x)^6+2*(5-x)^3 ?

The extreme (5-x)^6+2*(5-x)^3 is Saddle(5,0),Minimum(6,-1)

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extreme (5-x)^6+2*(5-x)^3

extreme

Saddle (5, 0), Minimum (6, - 1)

Solution steps

f^{'} (x) = 6 x^{5} - 150 x^{4} + 1500 x^{3} - 7506 x^{2} + 18810 x - 18900

Find intervals:

Decreasing

: - \infty < x < 5,

Decreasing

: 5 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = 5

into

(5 - x)^{6} + 2 \cdot (5 - x)^{3} : 0

Saddle (5, 0)

Plug

x = 6

into

(5 - x)^{6} + 2 \cdot (5 - x)^{3} : - 1

Minimum (6, - 1)

Saddle (5, 0), Minimum (6, - 1)

What is the extreme (5-x)^6+2*(5-x)^3 ?
The extreme (5-x)^6+2*(5-x)^3 is Saddle(5,0),Minimum(6,-1)