What is the extreme f(x)=2x^3+12x^2-30x ?

The extreme f(x)=2x^3+12x^2-30x is Maximum(-5,200),Minimum(1,-16)

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extreme f(x)=2x^3+12x^2-30x

extreme points

f (x) = 2 x^{3} + 12 x^{2} - 30 x

Maximum (- 5, 200), Minimum (1, - 16)

Solution steps

f^{'} (x) = 6 x^{2} + 24 x - 30

Find intervals:

Increasing

: - \infty < x < - 5,

Decreasing

: - 5 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 5

into

2 x^{3} + 12 x^{2} - 30 x : 200

Maximum (- 5, 200)

Plug

x = 1

into

2 x^{3} + 12 x^{2} - 30 x : - 16

Minimum (1, - 16)

Maximum (- 5, 200), Minimum (1, - 16)

- \frac{1}{3} cos (\frac{1}{3} x)

ln (x - 4)

\frac{1}{4} x^{3} - 2

f (x) = x - 6 - 6

(- 2, - 4), (4, 6)

What is the extreme f(x)=2x^3+12x^2-30x ?
The extreme f(x)=2x^3+12x^2-30x is Maximum(-5,200),Minimum(1,-16)