What is the extreme f(x)= 1/3 x^3-7x^2+24x+6 ?

The extreme f(x)= 1/3 x^3-7x^2+24x+6 is Maximum(2, 86/3),Minimum(12,-138)

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extreme f(x)= 1/3 x^3-7x^2+24x+6

extreme

Maximum (2, \frac{86}{3}), Minimum (12, - 138)

Solution steps

f^{'} (x) = x^{2} - 14 x + 24

Find intervals:

Increasing

: - \infty < x < 2,

Decreasing

: 2 < x < 12,

Increasing

: 12 < x < \infty

Plug

x = 2

into

\frac{1}{3} x^{3} - 7 x^{2} + 24 x + 6 : \frac{86}{3}

Maximum (2, \frac{86}{3})

Plug

x = 12

into

\frac{1}{3} x^{3} - 7 x^{2} + 24 x + 6 : - 138

Minimum (12, - 138)

Maximum (2, \frac{86}{3}), Minimum (12, - 138)

What is the extreme f(x)= 1/3 x^3-7x^2+24x+6 ?
The extreme f(x)= 1/3 x^3-7x^2+24x+6 is Maximum(2, 86/3),Minimum(12,-138)