The questions are in the photo below: I would like them all solved correctly.

6. Show that the function f(1:) =12613+8 satisfies the hypothesis of Rolle's Theorem on the closed interval [2. 4]. Find a number 6 between 2 and 4 such that f'(c) = 0. 7. A car covers 4km in 5 minutes. Using mathematics, explain why the speedometer must read exactly 48km/hr at some point during the trip. 8. (a) Write down Mean Value Theorem, remembering to include the conditions that 1' must satisfy for the theorem to hold. (b) Does the function f(:r:) = satisfy the conditions of the theorem on the interval [0, 16]? (c) Sketch a graph of the function f and the secant line from 1: = 0 to a: = 16. Estimate the point on the graph where the tangent line has the same slope as the secant line. (d) Use the Mean Value Theorem to find the exact value of m = c which, by the theorem, is guaranteed to exist in the given interval. Compare this with your estimate of c from part (c). 9. Evaluate the given limit without using L'H6pital's rule, and then check that your answer is correct using L'H6pital's rule. (a) 333% ('1) .E'Bw 3: Q: 10. Evaluate the following limits. Mini1:11 33612.: (C) 31132., t2 e\" (d) 131300 111?:1: 01' 93% 1:8; (f) 533} C2$+'1 (1' '13: :23: (h) .32.. 2