Determine whether f is differentiable at the given point.

if f '(a) exists, give its value. hint [see example 3.] (if an answer does not exist, enter dne.)

f(x) = x^1/5 + 7

a= 32

a=0

The average number of vehicles waiting in line to enter a parking lot can be modeled by the function f left parenthesis x right x squared over 2 left parenthesis 1 minus x right parenthesis endfraction , where x is a number between 0 and 1 known as the traffic intensity. find the rate of change of the number of vehicles waiting with respect to the traffic intensity for the intensities (a) xequals0.3 and (b) xequals0.6.