What is the extreme f(x)=x^3+2x^2-15x-20 ?

The extreme f(x)=x^3+2x^2-15x-20 is Maximum(-3,16),Minimum(5/3 ,-940/27)

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extreme f(x)=x^3+2x^2-15x-20

extreme points

f (x) = x^{3} + 2 x^{2} - 15 x - 20

Maximum (- 3, 16), Minimum (\frac{5}{3}, - \frac{940}{27})

Solution steps

f^{'} (x) = 3 x^{2} + 4 x - 15

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

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

Increasing

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

Plug

x = - 3

into

x^{3} + 2 x^{2} - 15 x - 20 : 16

Maximum (- 3, 16)

Plug

x = \frac{5}{3}

into

x^{3} + 2 x^{2} - 15 x - 20 : - \frac{940}{27}

Minimum (\frac{5}{3}, - \frac{940}{27})

Maximum (- 3, 16), Minimum (\frac{5}{3}, - \frac{940}{27})

What is the extreme f(x)=x^3+2x^2-15x-20 ?
The extreme f(x)=x^3+2x^2-15x-20 is Maximum(-3,16),Minimum(5/3 ,-940/27)