Question

Question #57a66

Answer 1

`b) f(x)=cos(x),c=pi/6`

Explanation:

We know:
`cos(pi/6)=sqrt3/2`

This means we can rewrite the limit like so:
`lim_(h->0)(cos(pi/6+h)-cos(pi/6))/h`

Considering the definition of a derivative of a function `f(x)` at a point `c`:
`lim_(h->0)(f(c+h)-f(c))/h`

A reasonable guess is that `c=pi \/ 6`, and using it, we can see that the inputs to the cosine function match up with the inputs to `f(x)` in the definition:
`lim_(h->0)(cos(color(red)(c+h))-cos(color(red)(c)))/h`

This means that if `c=pi \/ 6`, then `f(x)=cos(x)`.