# Thread: Log Equation -Increasing and Decreasing Function

1. ## Log Equation -Increasing and Decreasing Function

I need help with this question:

f(x) = sin(2x) + cos(2x) where x is an element of [0,pie].

Find the interval on which this function is increasing and decreasing.

I know that I must calculate f'(x) > 0 and f'(x) < 0

But I'm not good at differentiating trigonometric functions and at finding the intervals.

I would very grateful for any help.

2. ## Re: Log Equation -Increasing and Decreasing Function

Originally Posted by mlg
I need help with this question:
f(x) = sin(2x) + cos(2x) where x is an element of [0,pie].
Find the interval on which this function is increasing and decreasing.
OH please, we eat pie but pi , $\pi$, is a Greek letter,

$\\f'(x)=2\cos(2x)-2\sin(2x)\\f''(x)=-4\sin(2x)-4\cos(2x)$

3. ## Re: Log Equation -Increasing and Decreasing Function

Thank you.
I don't have the symbol 'pi' on my pc.
How do I deal with 'pi' to follow on from here?

4. ## Re: Log Equation -Increasing and Decreasing Function

Originally Posted by mlg
Thank you.
I don't have the symbol 'pi' on my pc.
How do I deal with 'pi' to follow on from here?
The point was the the correct spelling is pi not pie.

5. ## Re: Log Equation -Increasing and Decreasing Function

Originally Posted by mlg
Thank you.
I don't have the symbol 'pi' on my pc.
How do I deal with 'pi' to follow on from here?
Find where the derivative is zero. You will get a list of x-coordinates. Put them in order from least to greatest. Then the intervals to check are (0,x_1), (x_1,x_2), ..., (x_k,\pi) for however many intervals there are. Plug one value from each interval into the derivative. That will tell you the sign of the derivative on each interval.

6. ## Re: Log Equation -Increasing and Decreasing Function

Thanks.
Could anyone give an example on how to work out one of these intervals.

7. ## Re: Log Equation -Increasing and Decreasing Function

Example: Find where the derivative that Plato gave you is zero.