What is the extreme f(x)=5(x^2+4)^2(x-4)^3 ?

The extreme f(x)=5(x^2+4)^2(x-4)^3 is Saddle(4,0)

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extreme f(x)=5(x^2+4)^2(x-4)^3

extreme

Saddle (4, 0)

Solution steps

Find the critical points:

x = 4

Domain of

5 (x^{2} + 4)^{2} (x - 4)^{3} : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < 4,

Increasing

: 4 < x < \infty

Plug the extreme point

x = 4

into

5 (x^{2} + 4)^{2} (x - 4)^{3} \Rightarrow y = 0

Saddle (4, 0)

What is the extreme f(x)=5(x^2+4)^2(x-4)^3 ?
The extreme f(x)=5(x^2+4)^2(x-4)^3 is Saddle(4,0)