Question

Find the instantaneous rate of change at x=3

How do I do this without the function and only the graph?

Answer 1

The instantaneous rate of change at x=3 is the slope of the tangent line.

To answer this, you draw the tangent line and estimate the slope. In the picture, I drew my best estimate of what the tangent line at x=3 looks like. Based on that line, which has a slope of 1/2, I would stay the instantaneous rate of change is 1/2.

Without the formula, this is an estimate.