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

The extreme f(x)= 1/4 x^2+x^3-2 is Maximum(-1/6 ,-863/432),Minimum(0,-2)

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

extreme

Maximum (- \frac{1}{6}, - \frac{863}{432}), Minimum (0, - 2)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - \frac{1}{6},

Decreasing

: - \frac{1}{6} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{1}{6}

into

\frac{1}{4} x^{2} + x^{3} - 2 : - \frac{863}{432}

Maximum (- \frac{1}{6}, - \frac{863}{432})

Plug

x = 0

into

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

Minimum (0, - 2)

Maximum (- \frac{1}{6}, - \frac{863}{432}), Minimum (0, - 2)

What is the extreme f(x)= 1/4 x^2+x^3-2 ?
The extreme f(x)= 1/4 x^2+x^3-2 is Maximum(-1/6 ,-863/432),Minimum(0,-2)