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For what x, is the function f(x) = (7x-5)/(x+5) decreasing?  

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For what x, is the function f(x) = (7x-5)/(x+5) decreasing?

 

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The function f(x) = (7x-5)/(x+5)

For those values of x which make the first derivative of a function positive it is increasing and when the first derivative is negative it is decreasing.

f’(x) = -(7x – 5)/(x + 5)^2 + 7/(x + 5)

=> (5 – 7x + 7x + 35)/(x + 5)^2

=> 40/(x + 5)^2

It can be seen that 40/(x + 5)^2 is always positive.

Therefore the function (7x-5)/(x+5) is increasing for all values of x.

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