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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