Question: Let h, f be continuous functions on [4, 7] and differentiable functions on (4, 7). We consider the function F given by F(z) = det(C)

Let h, f be continuous functions on [4, 7] and differentiable functions on (4, 7). We consider the function F given by F(z) = det(C) where h(x) f(x) 12 +4 C = h(4) f(4) 20 h(7) f(7) 53 (a) Your classmate Kshitij asks you to find an x such that F(@) = 0. Enter your answer in the box below. One such value of r is I = (b) Your tutor Bhawan asks you to prove that there exists ce (4, 7) such that F'(c) =0. Provide your proof to your tutor Bhawan in the following essay box. Be sure to explain which theorems or results you use and how you use them

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