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

##### 1 Answer

Apr 14, 2016

Decreasing.

#### Explanation:

To determine if a function is increasing or decreasing at a point, use the function's derivative:

- If
#f'(a)<0# , then#f# is decreasing at#x=a# . - If
#f'(a)>0# , then#f# is increasing at#x=a# .

So, we first must find the derivative of **quotient rule**. Application of the quotient rule shows that

#f'(x)=(xd/dx(sinx)-sinxd/dx(x))/x^2#

#=(xcosx-sinx)/x^2#

So, to determine if

#f'(pi/3)=(pi/3cos(pi/3)-sin(pi/3))/(pi/3)^2#

#=(pi/3(1/2)-sqrt3/2)/(pi^2/9)approx-0.3123#

Since this is

We can check a graph of

graph{sinx/x [-3.945, 4.825, -1.568, 2.817]}