Consider the graph of the function f(x) = −x² + 5 (see figure).

(a) Find the equation of the secant line joining the points (−1, 4) and (2, 1).

(b) Use the Mean Value Theorem to determine a point c in the interval (−1, 2) such that the tangent line at c is parallel to the secant line.

(c) Find the equation of the tangent line through c.

(d) Use a graphing utility to graph f, the secant line, and the tangent line.

(-1,4), 11 - 4 6 2 -2 f(x)=-x+5 y M (2, 1) 2 4 x