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The curve C is defined by

y=ln⁡(sin⁡x−cos⁡x),π4<x<5π4
  1. Show that

    d2ydx2=1sin⁡2x−1
  2. The point P is the turning point of C. Find the coordinates of P, and determine whether this is a minimum or a maximum point.


For (b), you should use laws of logarithms first:

ln⁡(u)=12ln⁡(u)

Use the second derivative test!


The coordinates of P are of the form

(aπb,ln⁡(c)d),a,b,c,d∈N

If P is a minimum point, give 5abcd. If P is a maximum point, give 7abcd.