Suppose f: [0, 12] -> R is a piecewise-defined function f(z) = 24 - 12x+35 +8, if0 5 x 10 (px2 + qx tr, if 10 Equation A . A- Ix BIUSX x Styles Font Words: 0 (b) Suppose you are given some real number r. Select the correct statement below. There is no p and q such that f is differentiable at x = 10. There is a unique p and q such that f is differentiable at x = 10. There are infinitely many p and q such that f is differentiable at x = 10. Suppose r = 5. Find some values of p and q that work. If there is no such p and q, enter the word none. P, q= Syntax advice for (b) and (c): Enter your values in the correct order, exact values (no approximation), and separated by a comma. For example if your answer is p = 1/2 and q = 65 then just enter 1/2 , 65 (do not enter 65, 1/2) (c) Assume you are still given the real number r = 5 as above. Select the correct statement below. There is no p and q such that f is differentiable everywhere in [0, 12]. There is a unique p and q such that f is differentiable everywhere in [0, 12]. There are infinitely many p and q such that f is differentiable everywhere in [0, 12]. For this r that you are given, find some values of p and q that work. If there is no such p and q, enter the word none. P, q= (d) Briefly explain why there exists ro E Dom(f) for which f(x)