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# Given a function find where decreasing ?

Given f(x)=3x-2/x+5

Use interval notation, find where f(x) in decreasing?

For increasing I got negative infinity to negative five, union, negative five to positive infinity

### 3 Answers

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- Wayne DeguManLv 71 month ago
f(x) = (3x - 2)/(x + 5)

or, f(x) = 3(x + 5)/(x + 5) - 17/(x + 5)

so, f(x) = 3 - 17/(x + 5)

=> f(x) = 3 - 17(x + 5)⁻¹

Hence, f '(x) = 17/(x + 5)²

x = -5 is excluded from the domain

For values less than -5 or greater than 5, (x + 5)² is positive, so 17/(x + 5)² as positive.

So, for all values of the domain except x = -5, the function is increasing, i.e. never decreasing

A sketch is below.

:)>

- hayharbrLv 71 month ago
It's increasing everywhere except where it's undefined (at -5 ) so I agree; means it never decreases

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