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

The extreme f(x)=-5x+2x^2+(x^3)/3 is Maximum(-5, 100/3),Minimum(1,-8/3)

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

extreme points

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

Maximum (- 5, \frac{100}{3}), Minimum (1, - \frac{8}{3})

Solution steps

f^{'} (x) = - 5 + 4 x + x^{2}

Find intervals:

Increasing

: - \infty < x < - 5,

Decreasing

: - 5 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 5

into

- 5 x + 2 x^{2} + \frac{x ^{3}}{3} : \frac{100}{3}

Maximum (- 5, \frac{100}{3})

Plug

x = 1

into

- 5 x + 2 x^{2} + \frac{x ^{3}}{3} : - \frac{8}{3}

Minimum (1, - \frac{8}{3})

Maximum (- 5, \frac{100}{3}), Minimum (1, - \frac{8}{3})

7 x^{2} - 3

f (x) = 6 x + 2

4 x^{3} - 45 x^{2} + 150 x

x^{2} + 3 x - 5

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

What is the extreme f(x)=-5x+2x^2+(x^3)/3 ?
The extreme f(x)=-5x+2x^2+(x^3)/3 is Maximum(-5, 100/3),Minimum(1,-8/3)