Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 4x2 - 3x + 2, [0, 2] O Yes, it does not matter if f is continuous or differentiable, every function satifies the Mean Value Theorem. O Yes, fis continuous on [0, 2] and differentiable on (0, 2) since polynomials are continuous and differentiable on R. O No, f is not continuous on [0, 2]. O No, fis continuous on [0, 2] but not differentiable on (0, 2). O There is not enough information to verify if this function satifies the Mean Value Theorem. If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem. (Enter your answers as a comma-separated list. If it does not satisify the hypotheses, enter DNE). C =Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval?I x) : In x, [1! 9] 0 Yes, it does not matter if fis continuous or differentiable, every function satisfies the Mean Value Theorem. 0 Yes, fis continuous on [1, 9] and dierentiabie on {1, 9). O No, fis not continuous on [1r 9]. O No, fis continuous on [1, 9] but not differentiable on (1, 9). 0 There is not enough information to verify if this function satisfies the Mean Value Theorem. If it satisfies the hypotheses, find all numbers C that satisfy the conclusion of the Mean Value Theorem. [Enter your answers as a commasseparated list. If it does not satisfy the hypotheses, enter DNE). c: EXAMPLE 4 If an object moves in a straight line with position function 5 = fa), then the average velocity between t = a and t = b is b a b a and the velocity at t: r: is f'(c}. Thus the Mean Value Theorem tells us that at some time t = c between a and b the instantaneous velocity 1"(c) is equal to the average velocity. For instance, if a car traveled 1600 km in 20 hours, then the speedometer must have read \\:| kmfh at least once. In general, the Mean Value Theorem can be interpreted as saying that there is a number at which the instantaneous rate of change is equal to the average rate of change over an interval. Find the number C that satisfies the conclusion of the Mean Value Theorem on the given interval. x) = V}; [0, 25]