Which of the following are true about the production function?

a) When total product is at its maximum then average product lies above the marginal product

b) For a production function that is subject to increase returns to scale, followed by decreasing returns to scale, average product lies below the marginal product before the law of diminishing returns to labour sets in

c) When average product is at its maximum, then marginal product is also at a maximum

d) if a production function is subject to diminishing marginal returns at all stages of production, then the production function is concave function over all input values

e) Marginal product is the slope of a line that starts in the origin and forms a tangent to the total product curve