What is the extreme f(x)=6x^3-9x^2-216x+7 ?

The extreme f(x)=6x^3-9x^2-216x+7 is Maximum(-3,412),Minimum(4,-617)

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extreme f(x)=6x^3-9x^2-216x+7

extreme points

f (x) = 6 x^{3} - 9 x^{2} - 216 x + 7

Maximum (- 3, 412), Minimum (4, - 617)

Solution steps

f^{'} (x) = 18 x^{2} - 18 x - 216

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = - 3

into

6 x^{3} - 9 x^{2} - 216 x + 7 : 412

Maximum (- 3, 412)

Plug

x = 4

into

6 x^{3} - 9 x^{2} - 216 x + 7 : - 617

Minimum (4, - 617)

Maximum (- 3, 412), Minimum (4, - 617)

What is the extreme f(x)=6x^3-9x^2-216x+7 ?
The extreme f(x)=6x^3-9x^2-216x+7 is Maximum(-3,412),Minimum(4,-617)