Suppose f: [0, 13] R is a piecewise-defined function f(x) = { [|x 16x+60|+9, if0x11 pr+qx+r...

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Suppose f: [0, 13] R is a piecewise-defined function f(x) = { [|x 16x+60|+9, if0x11 pr+qx+r if 11 < x < 13. (a) Give a short proof why if 121 p + 11 q + r = 14, then fis continuous at x = = 11. a Equation Editor A- A-T B IU S x, x Styles Font Size 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 = 11. There is a unique p and q such that f is differentiable at x = 11. There are infinitely many p and q such that f is differentiable at x = 11. I Suppose r = -4. 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 = 1/8 and q = 4 then just enter 1/8, 4 (do not enter 4, 1/8) (c) Assume you are still given the real number r = -4 as above. Select the correct statement below. There is no p and q such that f is differentiable everywhere in [0, 13]. Suppose f: [0, 13] R is a piecewise-defined function f(x) = { [|x 16x+60|+9, if0x11 pr+qx+r if 11 < x < 13. (a) Give a short proof why if 121 p + 11 q + r = 14, then fis continuous at x = = 11. a Equation Editor A- A-T B IU S x, x Styles Font Size 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 = 11. There is a unique p and q such that f is differentiable at x = 11. There are infinitely many p and q such that f is differentiable at x = 11. I Suppose r = -4. 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 = 1/8 and q = 4 then just enter 1/8, 4 (do not enter 4, 1/8) (c) Assume you are still given the real number r = -4 as above. Select the correct statement below. There is no p and q such that f is differentiable everywhere in [0, 13].