Let X have the cdf F(x) = 1 − x−α, x ≥ 1. a. Find E(X) for those values of α for which E(X) exists. b. Find Var(X) for those values of α for which it exists

Find all points on the graph of, for which f′(x) = 0 and those for which f′(x) does not exist.

Below is a graph of f(x) discussed in the video. Since f(x) is positive on the interval (4,6), its antiderivative F(x) is ? on (4,6). Since f(x) is increasing on (4,6), F(x) is ? on (4,6).

Each of the following are composite functions of the form f(g(x)) . Identify the outer function f(x) , the inner function g(x) , and dy dx for each. a. y= 3   1+4x2 f(x)=       g(x)=       dy dx =     b. y=23x2+27x−110 f(x)=       g(x)=       dy dx =     c. y=(33x−1)73 f(x)=       g(x)=       dy dx =