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

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

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

extreme

Minimum (- 1, - \frac{3}{2}), Maximum (2, 3)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 1

into

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

Minimum (- 1, - \frac{3}{2})

Plug

x = 2

into

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

Maximum (2, 3)

Minimum (- 1, - \frac{3}{2}), Maximum (2, 3)

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