What is the extreme f(x)=2x(x+4)^3 ?

The extreme f(x)=2x(x+4)^3 is Saddle(-4,0),Minimum(-1,-54)

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extreme f(x)=2x(x+4)^3

extreme

Saddle (- 4, 0), Minimum (- 1, - 54)

Solution steps

f^{'} (x) = 2 ((x + 4)^{3} + 3 x (x + 4)^{2})

Find intervals:

Decreasing

: - \infty < x < - 4,

Decreasing

: - 4 < x < - 1,

Increasing

: - 1 < x < \infty

Plug

x = - 4

into

2 x (x + 4)^{3} : 0

Saddle (- 4, 0)

Plug

x = - 1

into

2 x (x + 4)^{3} : - 54

Minimum (- 1, - 54)

Saddle (- 4, 0), Minimum (- 1, - 54)

What is the extreme f(x)=2x(x+4)^3 ?
The extreme f(x)=2x(x+4)^3 is Saddle(-4,0),Minimum(-1,-54)