Question #2053

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

Expert's answer

<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.

As the first derivative of f(x) is positive on [0, pi/2], the function f(x) is increasing on this interval.

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