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## Homework Statement

The line x-2y+9=0 is tangent to the graph of y=f(x) at (3,6) and is also parallel to the line through (1,f(1)) and (5,f(5)). If f is differentiable on the closed interval [1,5] and f(1)=2, find f(5)

A) 2

B) 3

C) 4

D) 5

E) None of these

The correct answer is (C) 4

## The Attempt at a Solution

So I know the tangent line to (3,6) and f(5) have the same slope:

x-2y+9=0

2y=x+9

y=.5x+4.5

So, the slope is .5 at f(1), f(3), and f(5)

Now, I need to find the point at f(5). I do not know how to do this