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Finding tangent line

  • Thread starter physics604
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  • #1
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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=[itex]\frac{f(x)-f(a)}{x-a}[/itex]

The Attempt at a Solution



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

m=[itex]\frac{f(x)-f(a)}{x-a}[/itex]

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=[itex]\frac{f(x)-3)}{x-2}[/itex]

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

Any help would be greatly appreciated.
 

Answers and Replies

  • #2
jbunniii
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To be honest, I really don't know where to start. Here's what I have so far:

m=[itex]\frac{f(x)-f(a)}{x-a}[/itex]

I know slope is 4 according to the equation above.
What is the relationship between the slope of the tangent line and the derivative?
 
  • #3
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The slope -is- the derivative.
 
  • #4
jbunniii
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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
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I got it! Thanks!

f'(2) = 4 and f(2) = 3!
 
  • #7
jbunniii
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I got it! Thanks!

f'(2) = 4 and f(2) = 3!
Looks good. I'll take a look at your other question now.
 

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