Question

Is `f(x)= cot(3x+(5pi)/8)` increasing or decreasing at `x=pi/4`?

Answer 1

`f’(x)=-3csc((11pi)/(8))` will be increasing at `x=pi/4`

Explanation:

`f’(x)=-3csc(3x+((5pi)/8))`
For `x=pi/4`
`f’(x)=-3csc(((3pi)/4)+((5pi)/8))`
`f’(x)=-3csc((11pi)/8)`
As `csc((11pi)/(8))` falls in third quadrant and is negative,
`f’(x)=-3csc((11pi)/(8))` will be positive and hence is increasing.