B estimate the slope of the tangent line at p by

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(b) Estimate the slope of the tangent line atPby averaging the slopes of two adjacent secant lines. (Roundyour answer to one decimal place.)­96.3
6/5/2019hw02S2.13.11/11 points |Previous AnswersSCalcET8 2.1.AE.001.EXAMPLE 1Find an equation of the tangent line to the functionat the pointP(1,4).SOLUTIONWe will be able to find an equation of the tangent linetas soon as we know its slopem. The difficulty is that we know onlyone point,P, ont, whereas we need two points to compute the slope.But observe that we can compute an approximation tomby choosinga nearby pointon the graph (as in the figure) andcomputing the slopemPQof the secant linePQ. [Asecant line, fromthe Latin wordsecans, meaning cutting, is a line that cuts(intersects) a curve more than once.]y=4x4Q(x,4x4)x1QP.
3/10The graphs below illustrate the limiting process that occurs in thisexample. AsQapproachesPalong the graph, the corresponding

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Term
Spring
Professor
WAlker
Tags
Calculus, 10th Marine Regiment

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