A study on optimizing revenue from a website considered dividing customers into two groups based on a value of between 0 and 1, where z measures the proportion of the total bandwidth requested by a customer. Customers with a request less than z were considered low revenue, and those aboveェ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 attrbutes of the website and the customers.

(a) Find R'(x) and use it to find for what values of x in (0, 1).

(b) Find R"(x) and use it to find the point of diminishing returns. Also, state the intervals of concavity.