What is the extreme f(x)= 1/3 x^3+5x^2+24x+7 ?

The extreme f(x)= 1/3 x^3+5x^2+24x+7 is Maximum(-6,-29),Minimum(-4,-91/3)

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extreme f(x)= 1/3 x^3+5x^2+24x+7

extreme points

f (x) = \frac{1}{3} x^{3} + 5 x^{2} + 24 x + 7

Maximum (- 6, - 29), Minimum (- 4, - \frac{91}{3})

Solution steps

f^{'} (x) = x^{2} + 10 x + 24

Find intervals:

Increasing

: - \infty < x < - 6,

Decreasing

: - 6 < x < - 4,

Increasing

: - 4 < x < \infty

Plug

x = - 6

into

\frac{1}{3} x^{3} + 5 x^{2} + 24 x + 7 : - 29

Maximum (- 6, - 29)

Plug

x = - 4

into

\frac{1}{3} x^{3} + 5 x^{2} + 24 x + 7 : - \frac{91}{3}

Minimum (- 4, - \frac{91}{3})

Maximum (- 6, - 29), Minimum (- 4, - \frac{91}{3})

f (x) = \frac{x ^{2} - 16 x + 64}{x - 10}

f (x, y) = x^{2} + y^{2} - 6 x + 3 y

f (x) = x^{3} + y^{3} - 33 x y

f (x) = x^{3} - 2 x^{2} - 15 x + 3

f (x) = x^{3} - 2 x^{2} - 15 x + 5

What is the extreme f(x)= 1/3 x^3+5x^2+24x+7 ?
The extreme f(x)= 1/3 x^3+5x^2+24x+7 is Maximum(-6,-29),Minimum(-4,-91/3)