Using the MVT, find a value C for the function cosx - sinx on the interval [0, pi/2]
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Using the MVT, find a value C for the function cosx - sinx on the interval [0, pi/2]

[From: ] [author: ] [Date: 13-02-16] [Hit: ]
What am I doing wrong?[f(b) - f(a)] / (b - a) = f(c) for some c in the interval [0,pi/2].I think it should be 4/pi, not 2/pi. But anyway to solve this is difficult,......
Hi,
This is a non-calculator question.

I got stuck at cosx - sinx = 2/pi, after finding the mean and setting it equal to the original equation. I can't find any answer without a calculator.

What am I doing wrong?

-
the equation is
[f(b) - f(a)] / (b - a) = f'(c) for some c in the interval [0,pi/2].
[(cospi/2 - sinpi/2) - (cos0 - sin0)] / (pi/2 - 0) = -sinc - cosc
[-2]/(pi/2) = -sinc - cosc
4/pi = sinc + cosc
I think it should be 4/pi, not 2/pi. But anyway to solve this is difficult, I can't think of a way to do it without a calculator. There is an identity sinc + cosc = sqrt(2) * sin(c + pi/4) but it doesn't help in this case.
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