What is the extreme f(x)=39+6x+(54)/x ?

The extreme f(x)=39+6x+(54)/x is Maximum(-3,3),Minimum(3,75)

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extreme f(x)=39+6x+(54)/x

extreme

Maximum (- 3, 3), Minimum (3, 75)

Solution steps

f^{'} (x) = - \frac{54}{x ^{2}} + 6

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

39 + 6 x + \frac{54}{x} : 3

Maximum (- 3, 3)

Plug

x = 3

into

39 + 6 x + \frac{54}{x} : 75

Minimum (3, 75)

Maximum (- 3, 3), Minimum (3, 75)

What is the extreme f(x)=39+6x+(54)/x ?
The extreme f(x)=39+6x+(54)/x is Maximum(-3,3),Minimum(3,75)