Use the following graph of the function f(x) = 3x4 − x3 + 3x2 + x − 3 to answer this question: graph of 3 x to the fourth, minus x cubed, plus 3 x squared, plus x minus 3 what is the average rate of change from x = 0 to x = 1

Arandom sample of n = 25 observations is taken from a n(µ, σ ) population. a 95% confidence interval for µ was calculated to be (42.16, 57.84). the researcher feels that this interval is too wide. you want to reduce the interval to a width at most 12 units. a) for a confidence level of 95%, calculate the smallest sample size needed. b) for a sample size fixed at n = 25, calculate the largest confidence level 100(1 − α)% needed.