MATH 110 Lecture Notes - Lecture 44: Marginal Revenue, Income Distribution, Economic Surplus
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If we know the marginal revenue r "(x ) total revenue r(x) ? at any supply or demand level x , can we find the f " (x) Future and present values of an income stream. More generally, if we know the instantaneous rate of change. Define: a function of f is an antiderivative of f on an interval. I if f "(x )=f (x) for all x in. The function f(x )=x5+x4+5 x is an antiderivative of f (x)=5 x4+4 x3+5 since: Let g be an antiderivative of a function be of the form f. All antiderivatives of f (x)=4 x3+(1/ x)+ex are of the form f(x )=x4+lnx+ex+c. When finding an antiderivative, we are essentially reversing the process of computing a derivative. Have to learn how to take into account the sum, product, and chain rules when finding antiderivatives. Can always check your answer by computing its derivative. We use the symbol f (x)
