What is the extreme f(x)= 1/4 x^4+x^3-2 ?

The extreme f(x)= 1/4 x^4+x^3-2 is Minimum(-3,-35/4),Saddle(0,-2)

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extreme f(x)= 1/4 x^4+x^3-2

extreme

Minimum (- 3, - \frac{35}{4}), Saddle (0, - 2)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 3

into

\frac{1}{4} x^{4} + x^{3} - 2 : - \frac{35}{4}

Minimum (- 3, - \frac{35}{4})

Plug

x = 0

into

\frac{1}{4} x^{4} + x^{3} - 2 : - 2

Saddle (0, - 2)

Minimum (- 3, - \frac{35}{4}), Saddle (0, - 2)

What is the extreme f(x)= 1/4 x^4+x^3-2 ?
The extreme f(x)= 1/4 x^4+x^3-2 is Minimum(-3,-35/4),Saddle(0,-2)