Secant Line: Consider the function and the point on the graph of f.
(a) Graph f and the secant lines passing through P(2,8) and Q(x, f(x)) for x-values of 3,2,5, and 1,5.
(b) Find the slope of each secant line.
(c) Use the results of part (b) to estimate the slope of the tangent line to the graph of f at P(2,8). Describe how to improve your approximation of the slope.
(a) If P is the point on the graph of V, find the slopes of the secant lines PQ when Q is the point on the graph with .
(b) Estimate the slope of the tangent line at P by averaging the slopes of two secant lines.
(c) Use the graph of the function to estimate the slope of the tangent line at P. (This slope represents the rate at which the water is flowing from the tank after 15 minutes.)
