What is the extreme f(x)= 1/3 x^3+3x^2+5x-11/3 ?

The extreme f(x)= 1/3 x^3+3x^2+5x-11/3 is Maximum(-5, 14/3),Minimum(-1,-6)

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extreme f(x)= 1/3 x^3+3x^2+5x-11/3

extreme points

f (x) = \frac{1}{3} x^{3} + 3 x^{2} + 5 x - \frac{11}{3}

Maximum (- 5, \frac{14}{3}), Minimum (- 1, - 6)

Solution steps

f^{'} (x) = x^{2} + 6 x + 5

Find intervals:

Increasing

: - \infty < x < - 5,

Decreasing

: - 5 < x < - 1,

Increasing

: - 1 < x < \infty

Plug

x = - 5

into

\frac{1}{3} x^{3} + 3 x^{2} + 5 x - \frac{11}{3} : \frac{14}{3}

Maximum (- 5, \frac{14}{3})

Plug

x = - 1

into

\frac{1}{3} x^{3} + 3 x^{2} + 5 x - \frac{11}{3} : - 6

Minimum (- 1, - 6)

Maximum (- 5, \frac{14}{3}), Minimum (- 1, - 6)

f (x) = ∣ x ∣ + x^{2} - 5 x + 6

f (x, y) = 60 x^{\frac{1}{3}} y^{\frac{2}{3}}

x^{2} (x^{2} - 2)

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

- 3 x^{3}

What is the extreme f(x)= 1/3 x^3+3x^2+5x-11/3 ?
The extreme f(x)= 1/3 x^3+3x^2+5x-11/3 is Maximum(-5, 14/3),Minimum(-1,-6)