What is the extreme g(x)=x^3-x^2-8x-5 ?

The extreme g(x)=x^3-x^2-8x-5 is Maximum(-4/3 , 41/27),Minimum(2,-17)

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extreme g(x)=x^3-x^2-8x-5

extreme points

g (x) = x^{3} - x^{2} - 8 x - 5

Maximum (- \frac{4}{3}, \frac{41}{27}), Minimum (2, - 17)

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 - 5 : \frac{41}{27}

Maximum (- \frac{4}{3}, \frac{41}{27})

Plug

x = 2

into

x^{3} - x^{2} - 8 x - 5 : - 17

Minimum (2, - 17)

Maximum (- \frac{4}{3}, \frac{41}{27}), Minimum (2, - 17)

f (x) = \frac{x ^{2} + 1}{x ^{2} - 25}

2 x^{3} - x^{2} - 4 x + 4

f (x, y) = x^{2} + x y + y^{2} + 4 x - 7 y + 7

2 x^{3} - x^{2} - 4 x + 8

f (x) = x^{3} - 13 x^{2} - 9 x

What is the extreme g(x)=x^3-x^2-8x-5 ?
The extreme g(x)=x^3-x^2-8x-5 is Maximum(-4/3 , 41/27),Minimum(2,-17)