What is the extreme f(x)=2x^3+11x^2-8x-12 ?

The extreme f(x)=2x^3+11x^2-8x-12 is Maximum(-4,68),Minimum(1/3 ,-361/27)

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extreme f(x)=2x^3+11x^2-8x-12

extreme points

f (x) = 2 x^{3} + 11 x^{2} - 8 x - 12

Maximum (- 4, 68), Minimum (\frac{1}{3}, - \frac{361}{27})

Solution steps

f^{'} (x) = 6 x^{2} + 22 x - 8

Find intervals:

Increasing

: - \infty < x < - 4,

Decreasing

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

Increasing

: \frac{1}{3} < x < \infty

Plug

x = - 4

into

2 x^{3} + 11 x^{2} - 8 x - 12 : 68

Maximum (- 4, 68)

Plug

x = \frac{1}{3}

into

2 x^{3} + 11 x^{2} - 8 x - 12 : - \frac{361}{27}

Minimum (\frac{1}{3}, - \frac{361}{27})

Maximum (- 4, 68), Minimum (\frac{1}{3}, - \frac{361}{27})

f (x) = 4 x^{2} + 1 - 3 x

f (x) = 75 - x^{2}

f (x) = \frac{x ^{3}}{3} - 3 x^{2} + 8 x - 2, 0 \leq x \leq 3

f (x, y) = 2 x^{3} - 6 x y + 3 y^{2}

f (x) = ((45 - x) x - (10 + 24 x))

What is the extreme f(x)=2x^3+11x^2-8x-12 ?
The extreme f(x)=2x^3+11x^2-8x-12 is Maximum(-4,68),Minimum(1/3 ,-361/27)