What is the extreme f(x)=2x^3+4x^2+2x ?

The extreme f(x)=2x^3+4x^2+2x is Maximum(-1,0),Minimum(-1/3 ,-8/27)

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extreme f(x)=2x^3+4x^2+2x

extreme points

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

Maximum (- 1, 0), Minimum (- \frac{1}{3}, - \frac{8}{27})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

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

Increasing

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

Plug

x = - 1

into

2 x^{3} + 4 x^{2} + 2 x : 0

Maximum (- 1, 0)

Plug

x = - \frac{1}{3}

into

2 x^{3} + 4 x^{2} + 2 x : - \frac{8}{27}

Minimum (- \frac{1}{3}, - \frac{8}{27})

Maximum (- 1, 0), Minimum (- \frac{1}{3}, - \frac{8}{27})

f (x, y) = 80 x^{\frac{4}{10}} y^{\frac{2}{10}}

5 (x - 4)^{\frac{2}{3}}

f (x) = 5 x^{2} y + 3 x y^{8} + 23

f (x) = 5 x e^{- 4 x}

f (x) = f (x) = 5 + 54 x - 2 x^{3}, 0 \leq x \leq 4

What is the extreme f(x)=2x^3+4x^2+2x ?
The extreme f(x)=2x^3+4x^2+2x is Maximum(-1,0),Minimum(-1/3 ,-8/27)