What is the extreme f(x)=2x^3+24x^2+72x+7 ?

The extreme f(x)=2x^3+24x^2+72x+7 is Maximum(-6,7),Minimum(-2,-57)

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extreme f(x)=2x^3+24x^2+72x+7

extreme points

f (x) = 2 x^{3} + 24 x^{2} + 72 x + 7

Maximum (- 6, 7), Minimum (- 2, - 57)

Solution steps

f^{'} (x) = 6 x^{2} + 48 x + 72

Find intervals:

Increasing

: - \infty < x < - 6,

Decreasing

: - 6 < x < - 2,

Increasing

: - 2 < x < \infty

Plug

x = - 6

into

2 x^{3} + 24 x^{2} + 72 x + 7 : 7

Maximum (- 6, 7)

Plug

x = - 2

into

2 x^{3} + 24 x^{2} + 72 x + 7 : - 57

Minimum (- 2, - 57)

Maximum (- 6, 7), Minimum (- 2, - 57)

f (x, y) = 400 - 64 x^{2} - 36 y^{2}

x e^{\frac{( 5 - x )}{4}}

- x^{4} + 3 x^{3} - x^{2} - 5 x + 7

f (x) = - 3 x^{3} - 9

f (x) = - \frac{1}{2} x^{2} + 5 - 8

What is the extreme f(x)=2x^3+24x^2+72x+7 ?
The extreme f(x)=2x^3+24x^2+72x+7 is Maximum(-6,7),Minimum(-2,-57)