Follow these steps to calculate the value of the derivative of H(r) = e r

at the point r = 1.

a. Calculate the gradient H(r+h)−H(r)

h

(with r = 1) for different values of h, and complete the following table.

b. Plot the points in the table, and thus estimate the value of lim h→0 H(1 + h) − H(1)
h .

c. Sketch the graph of H(r) = e r and sketch (approximately)
the tangent to the graph at r = 1. Does your sketch agree with your answer in the previous part?