Economics Help pls

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Suppose you are given the following production function:
,

where y is output and K is capital.

y= 60K + 20.3K2- K3

1.1 what is a production function, what is the real work application of such, and where would you source the data to develop a production of the type given above.
1.2 Derive the average product of capital and the marginal product of capital.
1.3 How would you distinguish the equation above from a constant elasticity production function, a Cobb-Douglas production function, and a Leontief production function?
1.4 Finally, derive the points K and Y in which the MP of capital is equal to the minimum (or maximum) point on the average production curve.

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