## Elementary calculus for business, economics, and social sciences |

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Applied Example approach average cost bounded by f(x calculus change of base compute constant consumer surplus cost function cost of producing curve deﬁned deﬁnition determined dy/dx equation relating Example 15 Exercise FIGURE Find the area Find the derivative Find the equation Find the limit Find the maximum Find the slope Find the value ﬁnding ﬁrst partials Formula functional values given horizontal axis improper integral indeﬁnite integral independent variable intercept law of logarithms Let f(x linear marginal proﬁt maximum and minimum maximum proﬁt minimum point minimum value negative Nonexample number of units point-slope formula probability density function Problems proﬁt function rate of change rational functions real numbers region bounded respect restrictions revenue function Rule secant lines second derivative test selling price Solve sq units straight line Table tangent line undeﬁned units produced Values of Values vertical asymptote vertical lines write an equation yields zero