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.

Re: Log Equation -Increasing and Decreasing Function

Quote:

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 ,$\displaystyle \pi$, is a Greek letter,

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

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?

Re: Log Equation -Increasing and Decreasing Function

Quote:

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.

Re: Log Equation -Increasing and Decreasing Function

Quote:

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.

Re: Log Equation -Increasing and Decreasing Function

Thanks.

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

Re: Log Equation -Increasing and Decreasing Function

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