What is the extreme f(x)= 1/4 x+3+(400)/x ?

The extreme f(x)= 1/4 x+3+(400)/x is Maximum(-40,-17),Minimum(40,23)

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extreme f(x)= 1/4 x+3+(400)/x

extreme points

f (x) = \frac{1}{4} x + 3 + \frac{400}{x}

Maximum (- 40, - 17), Minimum (40, 23)

Solution steps

f^{'} (x) = - \frac{400}{x ^{2}} + \frac{1}{4}

Find intervals:

Increasing

: - \infty < x < - 40,

Decreasing

: - 40 < x < 0,

Decreasing

: 0 < x < 40,

Increasing

: 40 < x < \infty

Plug

x = - 40

into

\frac{1}{4} x + 3 + \frac{400}{x} : - 17

Maximum (- 40, - 17)

Plug

x = 40

into

\frac{1}{4} x + 3 + \frac{400}{x} : 23

Minimum (40, 23)

Maximum (- 40, - 17), Minimum (40, 23)

What is the extreme f(x)= 1/4 x+3+(400)/x ?
The extreme f(x)= 1/4 x+3+(400)/x is Maximum(-40,-17),Minimum(40,23)