A quadratic function is a function of the form: Q(x) = a.x + bx + c where a, b, c are constants. Let f(x) = COS x. (a) Find a quadratic function Q so that: f(0) = Q(0) and f'(0) = Q'(0) and f"(0) = Q"(0). The Q(x) you find is called a quadratic approximation of cos x at x = 0. After you have found Q(x) sketch y = cos x and y = Q(x) on the interval [-7/2, 7/2]. 1 = 1- 200 (b) Find an approximate solution to the equation cos(x) Hint: Solve the equation Q(x) =1- and note that cos(x) can be approximated by Q(x) whenever x is small.

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