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Calculus
Question

Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval?

$$\text{f}(x)=5x^2-2x+1,~[0,~2]$$

a. Yes, it does not matter If f is continuous or differentiable, every function satisfies the Mean Value Theorem.

b. Yes, f is continuous on [0, 2] and differentiable on (0, 2) since polynomials are continuous and differentiable on $$\mathbb{R}$$.

c. No, f is not continuous on [0, 2].

d. No, f is continuous on [0, 2] but not differentiable on (0, 2).

e. 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.

b. Yes, f is continuous on [0, 2] and differentiable on (0, 2) since polynomials are continuous and differentiable on $$\mathbb{R}$$.
$$c=1$$