What is the extreme f(x)=7x+5/(x+2) ?

The extreme f(x)=7x+5/(x+2) is Maximum(-sqrt(5/7)-2,-2sqrt(35)-14),Minimum(sqrt(5/7)-2,2sqrt(35)-14)

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extreme f(x)=7x+5/(x+2)

extreme points

f (x) = 7 x + \frac{5}{x + 2}

Maximum (- \frac{5}{7} - 2, - 235 - 14), Minimum (\frac{5}{7} - 2, 235 - 14)

Solution steps

f^{'} (x) = 7 - \frac{5}{( x + 2 ) ^{2}}

Find intervals:

Increasing

: - \infty < x < - \frac{14 + 35}{7},

Decreasing

: - \frac{14 + 35}{7} < x < - 2,

Decreasing

: - 2 < x < \frac{35 - 14}{7},

Increasing

: \frac{35 - 14}{7} < x < \infty

Plug

x = - \frac{5}{7} - 2

into

7 x + \frac{5}{x + 2} : - 235 - 14

Maximum (- \frac{5}{7} - 2, - 235 - 14)

Plug

x = \frac{5}{7} - 2

into

7 x + \frac{5}{x + 2} : 235 - 14

Minimum (\frac{5}{7} - 2, 235 - 14)

Maximum (- \frac{5}{7} - 2, - 235 - 14), Minimum (\frac{5}{7} - 2, 235 - 14)

What is the extreme f(x)=7x+5/(x+2) ?
The extreme f(x)=7x+5/(x+2) is Maximum(-sqrt(5/7)-2,-2sqrt(35)-14),Minimum(sqrt(5/7)-2,2sqrt(35)-14)