A differentiable function f is graphed on a coordinate grid. At the point P(1,3) on the curve, the unique tangent line visually passes through the additional grid point (3,7).
Assuming the viewing window uses one unit per grid square on both the x- and y-axes, address the following.
(1) Estimate f′(1) using the information given. Show your computation.
(2) Explain in one sentence what the value you found in part (a) represents about the behavior of f at x=1. Include units if appropriate.