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

The extreme f(x)=x^4+2x^3 is Minimum(-3/2 ,-27/16),Saddle(0,0)

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

extreme points

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

Minimum (- \frac{3}{2}, - \frac{27}{16}), Saddle (0, 0)

Solution steps

f^{'} (x) = 4 x^{3} + 6 x^{2}

Find intervals:

Decreasing

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

Increasing

: - \frac{3}{2} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{3}{2}

into

x^{4} + 2 x^{3} : - \frac{27}{16}

Minimum (- \frac{3}{2}, - \frac{27}{16})

Plug

x = 0

into

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

Saddle (0, 0)

Minimum (- \frac{3}{2}, - \frac{27}{16}), Saddle (0, 0)

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

e^{x^{2} - 7 x - 1}

f (x, y) = 5 - 2 x + 4 y - x^{2} - 4 y^{2}

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

What is the extreme f(x)=x^4+2x^3 ?
The extreme f(x)=x^4+2x^3 is Minimum(-3/2 ,-27/16),Saddle(0,0)