# How do you use #f(x) = sin(x^2-2)# to evaluate #(f(3.0002)-f(3))/0.0002#?

##### 1 Answer

May 12, 2018

Recall the derivative of a function is given by

#f'(x) = lim_(h-> 0) (f(x + h) - f(x))/h#

If we let

We can find the derivative using the chain rule

#f'(x)= 2xcos(x^2 - 2)#

#f'(3) = 2(3)cos(3^2 - 2) = 6cos(7) = 4.523#

If we plug the given expression into our calculator we get

#(f(3.0002) - f(3))/0.0002 = 4.521#

So our approximation is pretty good.

Hopefully this helps!