Calc 1 Help! For a certain graph y=f(x) the tangent line at the point (2,f(2)) goes through the points (3,2) and (5,-4). Find f(2) and f'(2)

Question

I am unsure of how to do this problem or even set it up. I didn't know whether to find the slope of the two points or not and was wondering if one of you all could help me. I would really appreciate it.

Answer 1

The slope of the tangent line = [2 - (-4)]/(3 -5) = -3; therefore, f'(2) = -3.

 

The tangent line is -3 = (y + 4)/(x-5), i.e. y = 11 - 3x and at x = 2, y = 5; therefore, f(2) = 5