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

##### 1 Answer

Jan 20, 2017

Decreasing.

#### Explanation:

Start by expanding

#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

Hopefully this helps!