What is the extreme f(x)=-2/3 x^3+2x^2+6x-50 ?

The extreme f(x)=-2/3 x^3+2x^2+6x-50 is Minimum(-1,-160/3),Maximum(3,-32)

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extreme f(x)=-2/3 x^3+2x^2+6x-50

extreme

Minimum (- 1, - \frac{160}{3}), Maximum (3, - 32)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 1

into

- \frac{2}{3} x^{3} + 2 x^{2} + 6 x - 50 : - \frac{160}{3}

Minimum (- 1, - \frac{160}{3})

Plug

x = 3

into

- \frac{2}{3} x^{3} + 2 x^{2} + 6 x - 50 : - 32

Maximum (3, - 32)

Minimum (- 1, - \frac{160}{3}), Maximum (3, - 32)

What is the extreme f(x)=-2/3 x^3+2x^2+6x-50 ?
The extreme f(x)=-2/3 x^3+2x^2+6x-50 is Minimum(-1,-160/3),Maximum(3,-32)