Thread: Open Intervals

For the function f(x)= 5x-7sin(x), 0<x<pi

I need to find the open interval(s) f is increasing and decreasing on.

I first found the derivative which is 5-7cos(x) and then found the zeros of the function which is arccos(5/7)

From this I found the increasing open interval to be ((arccos(5/7)),inf) and decreasing open interval to be (-inf, (arccos(5/7)))

Somehow this is incorrect could someone tell me what I did wrong?

Originally Posted by ctran

For the function f(x)= 5x-7sin(x), 0<x<pi

I need to find the open interval(s) f is increasing and decreasing on.

I first found the derivative which is 5-7cos(x) and then found the zeros of the function which is arccos(5/7)

From this I found the increasing open interval to be ((arccos(5/7)),inf) and decreasing open interval to be (-inf, (arccos(5/7)))

Somehow this is incorrect could someone tell me what I did wrong?

If your first derivative is positive then your function is increasing. If it is negative then your function is decreasing.

So if we are in the interval 0 < x < acs(5/7) is your derivative positive or negative? If we are in the interval acs(5/7) < x < pi is your derivative positive or negative?

-Dan