Question

Find the interval in which f(x)=sinx−cosx is increasing or decreasing?

Answer 1

There is no short answer.

Explanation:

To find to intervals which f(x) increases or decreases, we first need to find it's derivative.

`f(x) = sinx - cosx\\f'(x) = cosx - (-sinx) = cosx + sinx`

The function is increasing when it's value is > 0 and decreasing when it's value is < 0.

If we take a look at this graph, cosx+sinx is positive when they are both positive or when cosx is greater then sinx on the negative part.

I hope this answer helps.