Question

Given that the tangent line to the graph y=f(x) at the point (2,5) has the equation y=3x-1, find f '(2). Show steps please.

Answer 1

This is more of a concept question. When we find the derivative at a specific point such as 2, the answer is the slope of a tangent line at that point. You have the tangent line at (2,5), so what would f'(2) be?

Answer 2

From tangent line -> its slope
f'(2) = slope at x = 2

Answer 3

So I just take the derivative at x=2 or alternatively, y=5?

Answer 4

Can you read my post?

Answer 5

Do you know the equation of tangent line?

Answer 6

lim x-->a f(x) -f(a)/x-a

Answer 7

right?

Answer 8

Tangent line is just a linear line!

Answer 9

Yes.

Answer 10

I don't know what you mean.

Answer 11

Do you know slope- intercept form of linear equation ?

Answer 12

y=mx+b right?

Answer 13

Yes, what's m?

Answer 14

slope

Answer 15

So check your tangent line for m?

Answer 16

omg

Answer 17

lol

Answer 18

I got it now.

Answer 19

so f '(2) is asking what is the slope of the tangent line at x=2 right? Because I think that was what was confusing me. I dodn't understand the notation very well yet.

Answer 20

Oh, okay. So the derivation of something is just finding the slope of the tangent line?

Answer 21

Ah, seems so much easier now!
I feel like I will have more questions, but the concept is much clearer now.
Thank you so much!

Answer 22

So instantaneous rate of change means change in slope, right?

Answer 23

Right. Okay, here is another one I am sort of stuck on: Sketch the graph of a function f for which f(0)=-1. f '(0)=0, and f '(x) < 0 if x < 0, and f '(x)>0 if x > 0