Answer to Question #2053 in Calculus for vinay

Question

Prove that the function f, defined by f(x)=x sinx + cosx, is decreasing in [0,pi/2].

Answer 1

<img src="/cgi-bin/mimetex.cgi?f%27%28x%29%20=%20%5Csin%7Bx%7D%20+%20x%20%5Ccos%7Bx%7D%20-%20%5Csin%7Bx%7D%20=%20x%20%5Ccos%7Bx%7D" title="f'(x) = \sin{x} + x \cos{x} - \sin{x} = x \cos{x}">
As the first derivative of f(x) is positive on [0, pi/2], the function f(x) is increasing on this interval.