What is the extreme-2x^3-3x^2+12x ?

The extreme-2x^3-3x^2+12x is Minimum(-2,-20),Maximum(1,7)

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extreme-2x^3-3x^2+12x

extreme points

- 2 x^{3} - 3 x^{2} + 12 x

Minimum (- 2, - 20), Maximum (1, 7)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 2

into

- 2 x^{3} - 3 x^{2} + 12 x : - 20

Minimum (- 2, - 20)

Plug

x = 1

into

- 2 x^{3} - 3 x^{2} + 12 x : 7

Maximum (1, 7)

Minimum (- 2, - 20), Maximum (1, 7)

f (x) = 7 x - 7 sin (x), 0 \leq x \leq 2 π

f (x) = x^{4} + 12 x^{3} + 16 x^{2} + 4

f (x) = 4 x - x^{2} [1.5]

f (x) = 9 x y e^{- x^{2} - y^{2}}

f (x) = x^{3} - 12 x - 1

What is the extreme-2x^3-3x^2+12x ?
The extreme-2x^3-3x^2+12x is Minimum(-2,-20),Maximum(1,7)