1/2 points 1 Previous Answers SCaldET8 4.2.509.X Does the function satisfy the h

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1/2 points 1 Previous Answers SCaldET8 4.2.509.X Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? rx) = e-3x [0, 2] O Yes, fis continuous and differentiable on R, so it Is continuous on [o, 2] and differentiable on (0, 2) O Yes, It does not matter If f is continuous or differentiable; every function satisfes the Mean Value Theorem. O No, f is continuous on [O, 2] but not differentiable on (o, 2) O There is not enough Information to verify if this function satisfies the Mean Value Theorem. O No, f is not continuous on to, 2) If It satisfies the hypotheses, find all numbers c that satisty the conclusion of the Mean Value Theorem. (Enter your ans c= Need Help? ReaTaik to s Titor.

Explanation / Answer

c according to MVT is the number so that

f'(c)=-3e^{-3c}= (f(2)-f(0))/2= (exp(-6)-1)/2

e^{-3c}=(1-exp(-6))/2

-3c= ln(1-exp(-6))-ln(2)

c=ln(2)/3-ln(1- exp(6))/3

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