A study on optimizing revenue from a website considered dividing customers into two groups based on a value x between 0 and 1, where x measures the proportion of the total bandwidth requested by a customer. Customers with a request less than x were considered low revenue, and those above x high revenue. The expected revenue from the low revenue customers was described by R(x) = Cx(1 - e ^-kx), where C and k are positive constants based on attributes of the website and the customers.

(a) Find R′(x) and use it to find for what values of x in [0, 1] the revenue is increasing.
(b) Find R′(x) and use it to find for what values of x in [0, 1] the revenue function is concave up.