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Unformatted text preview: pen?) 4. Translating the English to the mathematics, we are being asked to find the average rate of change of R over the interval [100, 150]. We find ∆R R(150) − R(100) 3750 − 10000 = = = −125. ∆x 150 − 100 50 This means that we are losing $125 dollars of weekly revenue for each additional PortaBoy sold. (Can you think why this is possible?) We close this section with a new look at difference quotients, first introduced in Section 1.5. If we wish to compute the average rate of change of a function f over the interval [x, x + h], then we would have ∆f f (x + h) − f (x) f (x + h) − f (x) = = ∆x (x + h) − x h As we have indicated, the rate of change of a function (average or otherwise) is of great importance in Calculus.8 8 So, we are not torturing you with these for nothing. 2.1 Linear Functions 2.1.1 123 Exercises 1. Find both the point-slope form and the slope-intercept form of the line with the given slope which passes through the given point. √√ (a) m = 1 , P (−1, 4...
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