Math 31 Derivatives Project Mystery Curve In this activity, you will explore the meaning of continuity, differentiability, and other analytic features of a curve. Part I: To find the equation of your mystery curve, use the clues given below: The following five points lie on a function: (1, 20), (2, 4), (5, 3), (6, 2) and (10, 1). Find an equation that passes through these points and has the following features: three inflection points at least one local or relative maximum at least one local or relative minimum at least one critical point is not at a given point curve is continuous and differentiable throughout equation is not a single polynomial, but must be a piecewise defined function There are many possibilities that meet these criteria. Prove that your answer function does so. Part II: Follow the algorithm to sketch the curve f(x) = sin2(x) + cosx, 0 S X S 221'. domain and range x- and yintercepts symmetry (even, odd or neither) asymptotes (vertical, horizontal or slant/oblique) intervals of increase and/or decrease extrema points (local/relative and global/absolute) concavity points of inflection sketch of curve (graph provided on last page)