Consider the graph of the function f(x) = -x + 7 (see figure). (-1,6) -2 C...

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Consider the graph of the function f(x) = -x² + 7 (see figure). (-1,6) -2 C = y 8 2 (2,3) (a) Find the equation of the secant line joining the points (-1, 6) and (2, 3). 4 (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. -4 -2 À -2 2 -4 x -2 -2 2 4 Consider the graph of the function f(x) = -x² + 7 (see figure). (-1,6) -2 C = y 8 2 (2,3) (a) Find the equation of the secant line joining the points (-1, 6) and (2, 3). 4 (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. -4 -2 À -2 2 -4 x -2 -2 2 4