# Thread: Finding the derivative using the tangent line

1. ## Finding the derivative using the tangent line

If the line tangent to the graph of function f at the point (1,7) passes through the point (-2,-2), then f '(1) is: A)-5 B)1 C)3 D)7 E)undefined

I know that the slope of the tangent line is 3 using (y-y)/(x-x)
Also, I'm thinking that I have to use the mean value theorem but i'm not sure how to apply it to this problem

2. Originally Posted by rawkstar
If the line tangent to the graph of function f at the point (1,7) passes through the point (-2,-2), then f '(1) is: A)-5 B)1 C)3 D)7 E)undefined

I know that the slope of the tangent line is 3 using (y-y)/(x-x)
Also, I'm thinking that I have to use the mean value theorem but i'm not sure how to apply it to this problem

The slope of the tangent line to the graph of a derivable function $\displaystyle f(x)$ on a point $\displaystyle (x_1,f(x_1))$ on the graph is given by $\displaystyle f'(x_1)$.
You don't need mean value theorems or stuff: the answer is right in front of you.

Tonio

3. i'm not looking for the derivative of 1 of the tangent line, i need to find the derivative of 1 on the function f

4. Originally Posted by rawkstar
i'm not looking for the derivative of 1 of the tangent line, i need to find the derivative of 1 on the function f
The "derivative of 1" is always zero (0).

"y-y" also equals zero (0).

"x-x" also equals zero (0).

Why are you trying to do calculus if you don't remember how to calculate a slope? You have two points, simply calculate the slope and be done with it.

These are equivalent concepts:

1) Slope of the Tangent to the curve at x = c
2) Value of the derivative of the function evaluated at x = c.

Point-Slope Form

$\displaystyle (y-y_{1}) = f'(x_{1}) \cdot (x-x_{1})$

5. Originally Posted by rawkstar
i'm not looking for the derivative of 1 of the tangent line, i need to find the derivative of 1 on the function f

Read again my answer, or better: read again your book's definitions. You clearly don't understand the definition of tangent line to a (graph of a) function on some point of its graph.

Tonio