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

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

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

extreme points

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

Maximum (- 1, 0), Minimum (- \frac{1}{3}, - \frac{4}{27})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

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

Increasing

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

Plug

x = - 1

into

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

Maximum (- 1, 0)

Plug

x = - \frac{1}{3}

into

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

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

Maximum (- 1, 0), Minimum (- \frac{1}{3}, - \frac{4}{27})

x^{3} - 3 x^{2} + 3 x + 1

100 + \frac{1}{2} x + \frac{1800}{x}

- cos (x)

f (x) = 3 e^{x} - e^{3 x}

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

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