Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = 4x2 − 2x + 3, [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 double-struck r. 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).

ANSWER

Yes, f is continuous on [0, 2] and differentiable on (0, 2) since polynomials are continuous and differentiable on double-struck R.

EXPLANATION

We want to determine whether ,

satisfies the Mean Value Theorem, on the interval,

[0,2].

We check to see if the function satisfies all the hypotheses of the Mean Value Theorem.

1. The function is continuous on the closed interval, [0,2]

2. The function is differentiable on the open interval (0,2).

3. There is a c, such that,

Since the given function is a polynomial it is continuous on [0,2] and differentiable on (0,3) because polynomials are continuous and differentiable on the entire real numbers.

We now differentiate the function to obtain;

This implies that;

This implies that:

i think it is everything has to equal 180 so, if i correct 4=c. 6=d. 8=a. 7=b. and the last question would be c. because they are parallel lines and they are congruent.

step-by-step explanation:

the reason everything has to equal to 180 is because that is how it works. i'm guessing that is its rule. 4 and 8 are congruent and parallel so, that would be 30+30 because they have the same number. it would equal 60. 6 and 7 are congruent and parallel so, that would be 30+30 because they have the same number. it would equal 60. 60+60 is 180. so, now you have your answer

26

step-by-step explanation: