What is the extreme f(x)=2x^3+9x^2-24x ?

The extreme f(x)=2x^3+9x^2-24x is Maximum(-4,112),Minimum(1,-13)

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extreme f(x)=2x^3+9x^2-24x

extreme points

f (x) = 2 x^{3} + 9 x^{2} - 24 x

Maximum (- 4, 112), Minimum (1, - 13)

Solution steps

f^{'} (x) = 6 x^{2} + 18 x - 24

Find intervals:

Increasing

: - \infty < x < - 4,

Decreasing

: - 4 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 4

into

2 x^{3} + 9 x^{2} - 24 x : 112

Maximum (- 4, 112)

Plug

x = 1

into

2 x^{3} + 9 x^{2} - 24 x : - 13

Minimum (1, - 13)

Maximum (- 4, 112), Minimum (1, - 13)

f (x, y) = 2 x^{2} - 4 x + y^{2} - 8 y + 1

f (x) = \frac{x ^{3}}{3} - 6 x^{2}

f (x) = - x^{3} + 12 x - 14

f (x) = 200 - 8 y = 0

f (x) = (x - 5) ln (x - 5)

What is the extreme f(x)=2x^3+9x^2-24x ?
The extreme f(x)=2x^3+9x^2-24x is Maximum(-4,112),Minimum(1,-13)