What is the extreme f(x)= 1/3 x^3+11/2 x^2+24x+1 ?

The extreme f(x)= 1/3 x^3+11/2 x^2+24x+1 is Maximum(-8,-29/3),Minimum(-3,-61/2)

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extreme f(x)= 1/3 x^3+11/2 x^2+24x+1

extreme

Maximum (- 8, - \frac{29}{3}), Minimum (- 3, - \frac{61}{2})

Solution steps

f^{'} (x) = x^{2} + 11 x + 24

Find intervals:

Increasing

: - \infty < x < - 8,

Decreasing

: - 8 < x < - 3,

Increasing

: - 3 < x < \infty

Plug

x = - 8

into

\frac{1}{3} x^{3} + \frac{11}{2} x^{2} + 24 x + 1 : - \frac{29}{3}

Maximum (- 8, - \frac{29}{3})

Plug

x = - 3

into

\frac{1}{3} x^{3} + \frac{11}{2} x^{2} + 24 x + 1 : - \frac{61}{2}

Minimum (- 3, - \frac{61}{2})

Maximum (- 8, - \frac{29}{3}), Minimum (- 3, - \frac{61}{2})

What is the extreme f(x)= 1/3 x^3+11/2 x^2+24x+1 ?
The extreme f(x)= 1/3 x^3+11/2 x^2+24x+1 is Maximum(-8,-29/3),Minimum(-3,-61/2)