Given a function find where decreasing ?
Use interval notation, find where f(x) in decreasing?
For increasing I got negative infinity to negative five, union, negative five to positive infinity
- 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.
- Demiurge42Lv 71 month ago
f'(x) = 3 + 2/x^2
This is always positive so it is not decreasing anywhere.
- hayharbrLv 71 month ago
It's increasing everywhere except where it's undefined (at -5 ) so I agree; means it never decreases