An equation for the line tangent to the graph of the differentiable function f at x=2 is y=9x-12. Which of the following statements must be ?

Question

An equation for the line tangent to the graph of the differentiable function f at x=2 is y=9x-12. Which of the following statements must be ?

1. f(0) = -12
2. f(2) = 6
3. f' (2) = 9

*note that the third one is prime*

Answer choices

A) None

B) 1 and 2

C) 2 and 3

D) 1, 2, and 3

Answer 1

In order to answer this question you need to know the properties of a tangent line - the two important ones for this problem are that (1) the slope of the line tangent to f(x) at x=a is equal to the derivative of f(x) at x=a and (2) at the point of tangency, the tangent line and the original function "intersect" so they have the same y-value. You can tell information about the original function only at the point of tangency x=2 for this problem.