Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = 4x2 − 3x + 2, [0, 2] yes, it does not matter if f is continuous or differentiable, every function satifies the mean value theorem. yes, f is continuous on [0, 2] and differentiable on (0, 2) since polynomials are continuous and differentiable on . no, f is not continuous on [0, 2]. no, f is continuous on [0, 2] but not differentiable on (0, 2). 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).

a) Yes, f is continuous on [0, 2] and differentiable on (0, 2) since polynomials are continuous and differentiable on R

b) c=1

Step-by-step explanation:

a)The given function is;

For this function to satisfy the Mean Value Theorem, it must;

i) be continuous on [0,2]

ii)be differentiable on (0,2)

Since is a polynomial function, it is continuous on [0,2] and differentiable on (0,2) because polynomial functions are continuous and differentiable on the entire real numbers.

b)

Since the above two hypotheses are satisfied,it implies that, there is a certain such that;

Therefore the number that satisfies the conclusion of the Mean Value Theorem is c=1.

We can see from the graph that at x=1, the secant line is parallel to the tangent on the interval [0,2]

stops on an even number.