What is the extreme 2x^3+3x^2-72x ?

The extreme 2x^3+3x^2-72x is Maximum(-4,208),Minimum(3,-135)

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extreme 2x^3+3x^2-72x

extreme points

2 x^{3} + 3 x^{2} - 72 x

Maximum (- 4, 208), Minimum (3, - 135)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 4,

Decreasing

: - 4 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 4

into

2 x^{3} + 3 x^{2} - 72 x : 208

Maximum (- 4, 208)

Plug

x = 3

into

2 x^{3} + 3 x^{2} - 72 x : - 135

Minimum (3, - 135)

Maximum (- 4, 208), Minimum (3, - 135)

f (x, y) = 4 x^{2} - x y + 9 y^{2}

f (x) = 200 y^{2} + x^{2} - x^{2} y

f (x) = x^{4} - 4 x^{3} - x^{2} + 12 x - 2

f (x) = 5 x^{5} - 3 x^{2} + x - 10

f (x) = ln (x^{2} + x + 1), - 1 \leq x \leq 1

What is the extreme 2x^3+3x^2-72x ?
The extreme 2x^3+3x^2-72x is Maximum(-4,208),Minimum(3,-135)