Is #f(x)=sinx-cos(pi-x)# increasing or decreasing at #x=pi/3#?

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Answer 1 · 2017-01-20T22:39:46

Decreasing.

Start by expanding #cos(pi - x)#.

#f(x) = sinx- cospicosx + sinpisinx#

#f(x) = sinx - (-1cosx) + 0(sinx)#

#f(x) = sinx + cosx#

Differentiate:

#f'(x) = cosx - sinx#

Evaluate your point within the derivative.

#f(pi/3) = cos(pi/3) - sin(pi/3) = 1/2 - sqrt(3)/2 = (1 - sqrt(3))/2#

This is negative, so the function is decreasing at #x= pi/3#.

Hopefully this helps!