Homework Help: Finding tangent line

1. Oct 17, 2013

physics604

1. If an equation of the tangent line to the curve y=f(x) at the
point a=2 where is y=4x-5, find f(2) and f'(2).

2. Relevant equations

m=$\frac{f(x)-f(a)}{x-a}$

3. The attempt at a solution

To be honest, I really don't know where to start. Here's what I have so far:

m=$\frac{f(x)-f(a)}{x-a}$

I know slope is 4 according to the equation above. Also, I know there is a point (2,3), plugging a into the equation.

4=$\frac{f(x)-3)}{x-2}$

Now what can I do? This doesn't help me find f(2) or f'(2).

Any help would be greatly appreciated.

2. Oct 17, 2013

jbunniii

What is the relationship between the slope of the tangent line and the derivative?

3. Oct 17, 2013

physics604

The slope -is- the derivative.

4. Oct 17, 2013

jbunniii

OK, good. So you established that the slope of the tangent line at the point $x=2$ is $4$. What does that tell you about $f'(2)$?

5. Oct 17, 2013

physics604

I got it! Thanks!

f'(2) = 4 and f(2) = 3!

6. Oct 17, 2013

physics604

7. Oct 17, 2013

jbunniii

Looks good. I'll take a look at your other question now.