Callaway golf Company has determined that the marginal cost C of manufacturing x Big Bertha Golf clubs may be expressed by the quadratic function: C(x) = 4.9^2 - 617.4x + 19,600
How many clubs should be produced to minimize marginal cost?
That's solvable easily with calculus, not sure whether you're supposed to be using it given your heading:
C'(x) = 4.9(2)x - 617
= 9.8x -617.4
at its minimum,
9.8x = 617.4
To minimize the marginal cost, we need to find the minimum point of the quadratic function C(x) = 4.9x^2 - 617.4x + 19,600.
The minimum point of a quadratic function can be found using the formula x = -b / (2a), where a is the coefficient of the x^2 term, b is the coefficient of the x term, and x is the number of clubs to be produced.
In this case, the coefficient of the x^2 term is 4.9, and the coefficient of the x term is -617.4. Plugging these values into the formula, we get:
x = -(-617.4) / (2 * 4.9)
x = 617.4 / 9.8
x ≈ 63
Therefore, to minimize the marginal cost, approximately 63 clubs should be produced.