A firms short- run production function is given by Q = 1/2L2 for 0 L

Question:

A firm’s short- run production function is given by
Q = 1/2L2 for 0 ≤ L ≤ 2
And
Q = 3L – 1/4L2 for 2 < L ≤ 7.
a. Sketch the production function.
b. Find the maximum attainable production. How much labor is used at that level?
c. Identify the ranges of L utilization over which the marginal product of labor is increasing and decreasing.
d. Identify the range over which the marginal product of labor is negative.