A T-shirt manufacturer is planning to expand its workforce. It estimates that the number of T-shirts produced by hiring x new workers is given by:

T(x) = -0.25x4 + 5x3 0 < x < 15



a.) When is the rate of change of T-shirt production increasing and when is it decreasing?

b.) What is the point of diminishing returns and the maximum rate of change of T-shirt production?

c.) Sketch a graph of T and T' on the same coordinate system