What is the extreme 2x^3+6x^2-48x ?

The extreme 2x^3+6x^2-48x is Maximum(-4,160),Minimum(2,-56)

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extreme 2x^3+6x^2-48x

extreme points

2 x^{3} + 6 x^{2} - 48 x

Maximum (- 4, 160), Minimum (2, - 56)

Solution steps

f^{'} (x) = 6 x^{2} + 12 x - 48

Find intervals:

Increasing

: - \infty < x < - 4,

Decreasing

: - 4 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 4

into

2 x^{3} + 6 x^{2} - 48 x : 160

Maximum (- 4, 160)

Plug

x = 2

into

2 x^{3} + 6 x^{2} - 48 x : - 56

Minimum (2, - 56)

Maximum (- 4, 160), Minimum (2, - 56)

f (x) = - 2 x^{2} - 20 x + 8

f (x) = x^{5} - x^{3} + 1

y = \frac{x}{x ^{2} + 16}

- x^{3} (x - 3)

f (x) = \frac{4}{3} x^{3} - \frac{13}{2} x^{2} - 3 x + 11

What is the extreme 2x^3+6x^2-48x ?
The extreme 2x^3+6x^2-48x is Maximum(-4,160),Minimum(2,-56)