What is the extreme f(x)=x^3+x^2-5x-2 ?

The extreme f(x)=x^3+x^2-5x-2 is Maximum(-5/3 , 121/27),Minimum(1,-5)

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extreme f(x)=x^3+x^2-5x-2

extreme points

f (x) = x^{3} + x^{2} - 5 x - 2

Maximum (- \frac{5}{3}, \frac{121}{27}), Minimum (1, - 5)

Solution steps

f^{'} (x) = 3 x^{2} + 2 x - 5

Find intervals:

Increasing

: - \infty < x < - \frac{5}{3},

Decreasing

: - \frac{5}{3} < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - \frac{5}{3}

into

x^{3} + x^{2} - 5 x - 2 : \frac{121}{27}

Maximum (- \frac{5}{3}, \frac{121}{27})

Plug

x = 1

into

x^{3} + x^{2} - 5 x - 2 : - 5

Minimum (1, - 5)

Maximum (- \frac{5}{3}, \frac{121}{27}), Minimum (1, - 5)

f (x) = \frac{3}{4 x} - 5

f (x) = 2 - x^{2}, - 4 \leq x \leq 4

f (x) = - \frac{1}{4}

f (x) = \frac{8 x}{9 x - 1}

y = - \frac{x ^{3}}{x ^{2} - 4}

What is the extreme f(x)=x^3+x^2-5x-2 ?
The extreme f(x)=x^3+x^2-5x-2 is Maximum(-5/3 , 121/27),Minimum(1,-5)