MAC 2234 Study Guide - Midterm Guide: Random Variable, Riemann Sum, Standard Deviation
27 Sep 2020
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A function f is the antiderivative of f on an interval i if f"(x) = f(x) for all x in that interval. Example: 2x: antiderivative is x^2, any constant can be added to antiderivatives (because the derivative of any constant is, thus, the true antiderivative is x^2 + c. Example: suppose the marginal cost function of manufacturing x units of a product is c"(x) = 0. 06e^(0. 02x) and that the fixed cost is . C"(x) = 0. 06e^(0. 02x: c(x) = 0. 06/0. 02(e^(0. 02x), c(x) = 3e^(0. 02x) + c, we know the fixed cost is 9 when x = 0. Now we can solve for c: c(x) = 3e^(0. 02*0) + c = 9, c = 6. Marginal cost function is the derivative of the cost function s(t) 2nd derivative is acceleration. Now substitute back u = x^4 + 4. Substitution rule - if f"(x) = f(x), then f(u(x))u"(x)dx = f(u(x)) + c: undoing the chain rule. Change in x = (b a) / n.
