A professor at a university wants to estimate the average number of hours of sleep students get during exam week. On the first day of exams, she asked 20 students
how many hours they had slept the night before. The average of the sample was 5.88
with a standard deviation of 1.942. When estimating the average amount of sleep
with a 95% confidence interval, what is the margin of error?
1) 0.9089
2) 0.4342
3) 0.9058
4) 0.7509
5) 0.4508

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.