Calculus Optimization Error
A student seeks to minimize the cost function , where represents the number of units produced. To do so, the student calculates the derivative, , and sets it equal to 1. What is the primary error in this procedure?
A
The student’s mistake is in neglecting the constant term in the cost function during differentiation.
B
The student incorrectly set the derivative equal to 1; to find critical points, the derivative should be set equal to 0.
C
The mistake is that the cost function is quadratic and should be minimized using the vertex formula instead of differentiation.
D
The error arises because the derivative should be taken with respect to a different variable, not x.
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