Thread: Monotonically increasing

Here´s the question.



Ok so the derivative of f



The function is monotonically increasing if the derivative of f is bigger than zero in the interval. Or if

So my task should be to determine the lowest value of the right hand side of the inequality and say that alpha should be less than that? Is it so? I´ve tried that but ended up with zeros in the denominator and stuff. Any ideas?

min(cosx-1) in [0,pi/2] = -1

max(cosx-1) in [0,pi/2] = 0

Originally Posted by Also sprach Zarathustra

min(cosx-1) in [0,pi/2] = -1

max(cosx-1) in [0,pi/2] = 0

Yes. min(cosx-1) in [0,pi/2] =-1 and this happens as x --> pi/2 and therefore f´(0) larger than zero if



But what happens when x-->0 and how about all the other values between 0 and pi/2?

I´m still not sure how to choose alpha so that f´(x) is larger than zero in the interval.