APFIVE Experimental Procedure: A student is attempting to minimize the production cost in an optimization experiment. The cost function is given by $$C(x) = 0.5*x^2 - 10*x + 150$$, where x represents the number of units produced. To find the optimal value, the student differentiates C(x) and sets $$C'(x) = 1$$ instead of setting it equal to 0. What is the mistake in this procedure?
The error arises because the derivative should be taken with respect to a different variable, not x.
The mistake is that the cost function is quadratic and should be minimized using the vertex formula instead of differentiation.
The student incorrectly set the derivative equal to 1; to find critical points, the derivative should be set equal to 0.
The student’s mistake is in neglecting the constant term in the cost function during differentiation.
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