# Finding tangent line

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).

## Homework Equations

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

## 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.

jbunniii
Homework Helper
Gold Member
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.
What is the relationship between the slope of the tangent line and the derivative?

The slope -is- the derivative.

jbunniii
Homework Helper
Gold Member
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)##?

I got it! Thanks!

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

jbunniii