let f(x)=sin(x)+cos(x)+tan(x)+arcsin(x)+arccos(x)+arctan(x).

Question

If M&m are maximum and minimum values of f(x), then thier arithmetic mean is equal to

 

Answer 1

  At first, I took the derivative (don't even know if you know what that is) and set it to zero. two of the 3 answers lead to pi/2 and 3pi/2. Then I laughed at myself. Because of the tangent in your function, the entire function has asymptotes at these 2 values. That means it goes up to infinity and down to negativ infinity. Not that you can really take the average of these 2 concept numbers, but if you add them together, I suppose you'd get zero, then divide by 2 and get zero. Makes sense to me.