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

The extreme f(x)=x^3-5/2 x^2-2x is Maximum(-1/3 , 19/54),Minimum(2,-6)

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

extreme points

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

Maximum (- \frac{1}{3}, \frac{19}{54}), Minimum (2, - 6)

Solution steps

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

Find intervals:

Increasing

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

Decreasing

: - \frac{1}{3} < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - \frac{1}{3}

into

x^{3} - \frac{5}{2} x^{2} - 2 x : \frac{19}{54}

Maximum (- \frac{1}{3}, \frac{19}{54})

Plug

x = 2

into

x^{3} - \frac{5}{2} x^{2} - 2 x : - 6

Minimum (2, - 6)

Maximum (- \frac{1}{3}, \frac{19}{54}), Minimum (2, - 6)

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

f (x, y) = x^{3} - 12 x - y^{2} - 8 y + 18

f (x) = 45 x + y

f (x) = 2 x^{3} - 9 x^{2} + 12 x + 7

f (x) = 2 x^{3} - 9 x^{2} + 12 x + 1

What is the extreme f(x)=x^3-5/2 x^2-2x ?
The extreme f(x)=x^3-5/2 x^2-2x is Maximum(-1/3 , 19/54),Minimum(2,-6)