What is the extreme f(x)=2x^3+12x^2-72x+11 ?

The extreme f(x)=2x^3+12x^2-72x+11 is Maximum(-6,443),Minimum(2,-69)

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extreme f(x)=2x^3+12x^2-72x+11

extreme points

f (x) = 2 x^{3} + 12 x^{2} - 72 x + 11

Maximum (- 6, 443), Minimum (2, - 69)

Solution steps

f^{'} (x) = 6 x^{2} + 24 x - 72

Find intervals:

Increasing

: - \infty < x < - 6,

Decreasing

: - 6 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 6

into

2 x^{3} + 12 x^{2} - 72 x + 11 : 443

Maximum (- 6, 443)

Plug

x = 2

into

2 x^{3} + 12 x^{2} - 72 x + 11 : - 69

Minimum (2, - 69)

Maximum (- 6, 443), Minimum (2, - 69)

What is the extreme f(x)=2x^3+12x^2-72x+11 ?
The extreme f(x)=2x^3+12x^2-72x+11 is Maximum(-6,443),Minimum(2,-69)