# Thread: Finding coordinates on a tangent line.

1. ## Finding coordinates on a tangent line.

I apologize if the image is a little hard to see. But that's the image given in the problem and it goes like this:

"The function has f(4) = 25 and f'(4) = 1.5. Find the coordinates of the points A, B, and C."

In case you can't see it, along the x-axis, point C is at 3.9, point A is at 4, and point B is at 4.2.

Any help on how to do this, please?

2. Equation of the tangent line at (a,f(a)):

y = f ' (a) (x-a) +f(a)

y= 1.5 (x-4) + 25

you should now be able to answer the question

3. Originally Posted by Rumor

I apologize if the image is a little hard to see. But that's the image given in the problem and it goes like this:

"The function has f(4) = 25 and f'(4) = 1.5. Find the coordinates of the points A, B, and C."

In case you can't see it, along the x-axis, point C is at 3.9, point A is at 4, and point B is at 4.2.

Any help on how to do this, please?
As f(4) = 25 and we're given f '(4) ==> (4,25) is the tangency point and thus it belongs to the tangent line of f at (4,25) ==> this line passes thorugh (4,25) and its slope is f '(4) = 1.5, so its equation is:

y - 25 = 1.5(x - 4) ==> y = 1.5x + 19

Well, now just plg in x = 3.9 and x = 4.2 to find out the y-coordinate of points C and B, resp.

Tonio