Consider the function f (x) = −x2 + 4x − 3. Find the average rate of change of the function from x1 to x2.
(a) x1 = 1, x2 = 2
(b) x1 = 1, x2 = 1.5
(c) x1 = 1, x2 = 1.25
(d) x1 = 1, x2 = 1.125
(e) x1 = 1, x2 = 1.0625
(f) Does the average rate of change seem to be approaching one value? If so, state the value.
(g) Find the equations of the secant lines through the points {x1, f (x1)} and {x2, f (x2)} for parts (a)-(e).
(h) Find the equation of the line through the point {1, f (1)} using your answer from part (f) as the slope of the line.