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

Mathematics

1 answer:

alisha [4.7K]3 years ago

3 0

Answer:

There is no short answer.

Step-by-step 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.

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