# Finding the derivative using the tangent line

• Dec 12th 2009, 10:26 AM
rawkstar
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
• Dec 12th 2009, 11:20 AM
tonio
Quote:

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 $f(x)$ on a point $(x_1,f(x_1))$ on the graph is given by $f'(x_1)$.
You don't need mean value theorems or stuff: the answer is right in front of you.

Tonio
• Dec 12th 2009, 11:31 AM
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
• Dec 12th 2009, 11:55 AM
TKHunny
Quote:

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

$(y-y_{1}) = f'(x_{1}) \cdot (x-x_{1})$
• Dec 12th 2009, 12:11 PM
tonio
Quote:

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