Attempt any one of the following: a

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Attempt any one of the following: a. Show that the function ff given by f(x)=tan⁡−1(sin⁡x+cos⁡x)f(x) = \tan^{-1}(\sin x + \cos x), x>0x > 0 is always a strictly increasing function in (0,π4)\left(0, \frac{\pi}{4}\right) b. An open box is to be constructed by removing equal squares from each corner of a 3 metre by 8 metre rectangular sheet of aluminium and folding up the sides. Find the volume of the largest such box.

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