What is the extreme-6x^3+3x^2+12x-2 ?

The extreme-6x^3+3x^2+12x-2 is Minimum(-2/3 ,-62/9),Maximum(1,7)

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extreme-6x^3+3x^2+12x-2

extreme points

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

Minimum (- \frac{2}{3}, - \frac{62}{9}), Maximum (1, 7)

Solution steps

f^{'} (x) = - 18 x^{2} + 6 x + 12

Find intervals:

Decreasing

: - \infty < x < - \frac{2}{3},

Increasing

: - \frac{2}{3} < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - \frac{2}{3}

into

- 6 x^{3} + 3 x^{2} + 12 x - 2 : - \frac{62}{9}

Minimum (- \frac{2}{3}, - \frac{62}{9})

Plug

x = 1

into

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

Maximum (1, 7)

Minimum (- \frac{2}{3}, - \frac{62}{9}), Maximum (1, 7)

f (x) = 5 - 3 x

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

f (x) = ∣ x ∣ - 1

2 y = 4 x^{2} - 5

f (x) = 3^{x + 2}

What is the extreme-6x^3+3x^2+12x-2 ?
The extreme-6x^3+3x^2+12x-2 is Minimum(-2/3 ,-62/9),Maximum(1,7)