What is the extreme f(x)= 1/3 x^3-x^2-8x+1 ?

The extreme f(x)= 1/3 x^3-x^2-8x+1 is Maximum(-2, 31/3),Minimum(4,-77/3)

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extreme f(x)= 1/3 x^3-x^2-8x+1

extreme points

f (x) = \frac{1}{3} x^{3} - x^{2} - 8 x + 1

Maximum (- 2, \frac{31}{3}), Minimum (4, - \frac{77}{3})

Solution steps

f^{'} (x) = x^{2} - 2 x - 8

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = - 2

into

\frac{1}{3} x^{3} - x^{2} - 8 x + 1 : \frac{31}{3}

Maximum (- 2, \frac{31}{3})

Plug

x = 4

into

\frac{1}{3} x^{3} - x^{2} - 8 x + 1 : - \frac{77}{3}

Minimum (4, - \frac{77}{3})

Maximum (- 2, \frac{31}{3}), Minimum (4, - \frac{77}{3})

x^{2} + 7

- \frac{31}{( 6 + t ) ^{2}}

y = x^{x^{x}}

f (x) = \frac{3 x}{x - 4}

f (x) = 2 x + 5

What is the extreme f(x)= 1/3 x^3-x^2-8x+1 ?
The extreme f(x)= 1/3 x^3-x^2-8x+1 is Maximum(-2, 31/3),Minimum(4,-77/3)