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 "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