What is the extreme 1/3 x^3+3x^2+5x ?

The extreme 1/3 x^3+3x^2+5x is Maximum(-5, 25/3),Minimum(-1,-7/3)

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extreme 1/3 x^3+3x^2+5x

extreme points

\frac{1}{3} x^{3} + 3 x^{2} + 5 x

Maximum (- 5, \frac{25}{3}), Minimum (- 1, - \frac{7}{3})

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{25}{3}

Maximum (- 5, \frac{25}{3})

Plug

x = - 1

into

\frac{1}{3} x^{3} + 3 x^{2} + 5 x : - \frac{7}{3}

Minimum (- 1, - \frac{7}{3})

Maximum (- 5, \frac{25}{3}), Minimum (- 1, - \frac{7}{3})

f (x) = - 4 cos (2 x)

f (x) = \frac{1}{5} cos (3 x - π)

f (x) = \frac{9 x - 3}{x - 1}

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

f (x) = x^{3} + 4

What is the extreme 1/3 x^3+3x^2+5x ?
The extreme 1/3 x^3+3x^2+5x is Maximum(-5, 25/3),Minimum(-1,-7/3)