Does the function satisfy the hypotheses ofthe Mean Value Theoremonthegiven inte

Question

Does the function satisfy the hypotheses ofthe Mean Value Theoremonthegiven interval? O Yes, itdoes not matter iffis continuous or differentiable, every function satifies the Mean Value Theorem. O Yes, fiscontinuous on [0,2] and differentiable on (0,2) since polynomials are continuous and differentiable on R. O No fis not continuous on (0,2. O No fiscontinuous onto, 2 but not differentiable on (0,2). O There is not enough information to verify if this function satifies the Mean value Theorem. fit 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).

Explanation / Answer

given f(x)=5x^2-2x+1, [0,2]

yes, f is continous on [0,2] and differetiable on [0,2] since polynomials are continous and deffrentiable om R

then f'(c) = [ f(b) - f(c) ]/(b-a)

10c - 2 = [ 17 - 1]/(2-0)

10c = 10

c = 1

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