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

The extreme f(x)=x^3-x^2-8x+1 is Maximum(-4/3 , 203/27),Minimum(2,-11)

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

extreme points

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

Maximum (- \frac{4}{3}, \frac{203}{27}), Minimum (2, - 11)

Solution steps

f^{'} (x) = 3 x^{2} - 2 x - 8

Find intervals:

Increasing

: - \infty < x < - \frac{4}{3},

Decreasing

: - \frac{4}{3} < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - \frac{4}{3}

into

x^{3} - x^{2} - 8 x + 1 : \frac{203}{27}

Maximum (- \frac{4}{3}, \frac{203}{27})

Plug

x = 2

into

x^{3} - x^{2} - 8 x + 1 : - 11

Minimum (2, - 11)

Maximum (- \frac{4}{3}, \frac{203}{27}), Minimum (2, - 11)

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

y = \frac{x ^{2} + 10 x + 9}{x ^{2} + 2 x + 1}

f (x) = x^{3} - x^{2} - 8 x - 2

2 x e^{- x}

f (y) = 7 x - x^{2} + 18

What is the extreme f(x)=x^3-x^2-8x+1 ?
The extreme f(x)=x^3-x^2-8x+1 is Maximum(-4/3 , 203/27),Minimum(2,-11)