What is the extreme f(x)= 2/3 x^3-x^2-12x+3 ?

The extreme f(x)= 2/3 x^3-x^2-12x+3 is Maximum(-2, 53/3),Minimum(3,-24)

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extreme f(x)= 2/3 x^3-x^2-12x+3

extreme points

f (x) = \frac{2}{3} x^{3} - x^{2} - 12 x + 3

Maximum (- 2, \frac{53}{3}), Minimum (3, - 24)

Solution steps

f^{'} (x) = 2 x^{2} - 2 x - 12

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 2

into

\frac{2}{3} x^{3} - x^{2} - 12 x + 3 : \frac{53}{3}

Maximum (- 2, \frac{53}{3})

Plug

x = 3

into

\frac{2}{3} x^{3} - x^{2} - 12 x + 3 : - 24

Minimum (3, - 24)

Maximum (- 2, \frac{53}{3}), Minimum (3, - 24)

What is the extreme f(x)= 2/3 x^3-x^2-12x+3 ?
The extreme f(x)= 2/3 x^3-x^2-12x+3 is Maximum(-2, 53/3),Minimum(3,-24)