Pete’s parents are offering to pay him a weekly allowance for doing his chores. they’ve given him two different payment options for a period of 15 weeks.

option 1: $20 every week

option 2: a penny in the first week, and then double the amount from the previous week in each week after that. so, 1 penny in the first week, 2 pennies in the second week, 4 pennies in the third week, and so on.

which one is the better option for pete? explain why.

Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = 4x^2 + 3x + 4, [−1, 1] no, f is continuous on [−1, 1] but not differentiable on (−1, 1). no, f is not continuous on [−1, 1]. yes, f is continuous on [−1, 1] and differentiable on (−1, 1) since polynomials are continuous and differentiable on . there is not enough information to verify if this function satisfies the mean value theorem. yes, it does not matter if f is continuous or differentiable; every function satisfies the mean value theorem.