Finding f(2) and f'(2) given tangent line y=4x-5 at x=2

[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).

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]

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?

 

[physics604]

The slope -is- the derivative.

 

[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 $f'(2)$?

 

[physics604]

I got it! Thanks!

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

 

[physics604]

Can you help me with another question I have? Thanks!

https://www.physicsforums.com/showthread.php?p=4542320#post4542320

 

[jbunniii]

I got it! Thanks!

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

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