What is the extreme f(x)= 1/3 x^3+5/2 x^2-24x+2 ?

The extreme f(x)= 1/3 x^3+5/2 x^2-24x+2 is Maximum(-8, 550/3),Minimum(3,-77/2)

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extreme f(x)= 1/3 x^3+5/2 x^2-24x+2

extreme

Maximum (- 8, \frac{550}{3}), Minimum (3, - \frac{77}{2})

Solution steps

f^{'} (x) = x^{2} + 5 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{5}{2} x^{2} - 24 x + 2 : \frac{550}{3}

Maximum (- 8, \frac{550}{3})

Plug

x = 3

into

\frac{1}{3} x^{3} + \frac{5}{2} x^{2} - 24 x + 2 : - \frac{77}{2}

Minimum (3, - \frac{77}{2})

Maximum (- 8, \frac{550}{3}), Minimum (3, - \frac{77}{2})

What is the extreme f(x)= 1/3 x^3+5/2 x^2-24x+2 ?
The extreme f(x)= 1/3 x^3+5/2 x^2-24x+2 is Maximum(-8, 550/3),Minimum(3,-77/2)