What is the extreme f(x)= 1/3 x^3+13/2 x^2+42x+3 ?

The extreme f(x)= 1/3 x^3+13/2 x^2+42x+3 is Maximum(-7,-521/6),Minimum(-6,-87)

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extreme f(x)= 1/3 x^3+13/2 x^2+42x+3

extreme

Maximum (- 7, - \frac{521}{6}), Minimum (- 6, - 87)

Solution steps

f^{'} (x) = x^{2} + 13 x + 42

Find intervals:

Increasing

: - \infty < x < - 7,

Decreasing

: - 7 < x < - 6,

Increasing

: - 6 < x < \infty

Plug

x = - 7

into

\frac{1}{3} x^{3} + \frac{13}{2} x^{2} + 42 x + 3 : - \frac{521}{6}

Maximum (- 7, - \frac{521}{6})

Plug

x = - 6

into

\frac{1}{3} x^{3} + \frac{13}{2} x^{2} + 42 x + 3 : - 87

Minimum (- 6, - 87)

Maximum (- 7, - \frac{521}{6}), Minimum (- 6, - 87)

What is the extreme f(x)= 1/3 x^3+13/2 x^2+42x+3 ?
The extreme f(x)= 1/3 x^3+13/2 x^2+42x+3 is Maximum(-7,-521/6),Minimum(-6,-87)