What is the extreme f(x)=-6(x^2+81)(x-5)^3 ?

The extreme f(x)=-6(x^2+81)(x-5)^3 is Saddle(5,0)

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extreme f(x)=-6(x^2+81)(x-5)^3

extreme

Saddle (5, 0)

Solution steps

Find the critical points:

x = 5

Domain of

- 6 (x^{2} + 81) (x - 5)^{3} : - \infty < x < \infty

Find intervals:

Decreasing

: - \infty < x < 5,

Decreasing

: 5 < x < \infty

Plug the extreme point

x = 5

into

- 6 (x^{2} + 81) (x - 5)^{3} \Rightarrow y = 0

Saddle (5, 0)

What is the extreme f(x)=-6(x^2+81)(x-5)^3 ?
The extreme f(x)=-6(x^2+81)(x-5)^3 is Saddle(5,0)