Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = e−5x, [0, 3] yes, f is continuous and differentiable on double-struck r, so it is continuous on [0, 3] and differentiable on (0, 3) . no, f is continuous on [0, 3] but not differentiable on (0, 3). there is not enough information to verify if this function satisfies the mean value theorem. no, f is not continuous on [0, 3]. yes, it does not matter if f is continuous or differentiable; every function satisfies the mean value theorem.

Each of the following data sets has a mean of x = 10. (i) 8 9 10 11 12 (ii) 7 9 10 11 13 (iii) 7 8 10 12 13 (a) without doing any computations, order the data sets according to increasing value of standard deviations. (i), (iii), (ii) (ii), (i), (iii) (iii), (i), (ii) (iii), (ii), (i) (i), (ii), (iii) (ii), (iii), (i) (b) why do you expect the difference in standard deviations between data sets (i) and (ii) to be greater than the difference in standard deviations between data sets (ii) and (iii)? hint: consider how much the data in the respective sets differ from the mean. the data change between data sets (i) and (ii) increased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). the data change between data sets (ii) and (iii) increased the squared difference îł(x - x)2 by more than data sets (i) and (ii). the data change between data sets (i) and (ii) decreased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). none of the above