# 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.