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Which of the following do you think is closest to the temperature at 5:15am ?A= 2.5oFB= 52oFC= 43.5oFD= 44.5oFE= 5.15oF
(8.6) Tangent Line ApproximationAt 5am the temperature is 42oFand increasing at a rate of 10oFper hour.Which of the following do you think is closest to the temperature at 5:15am ?A= 2.5oFB= 52oFC= 43.5oFD= 44.5oFE= 5.15oFD5:15 is 1/4 of an hour after 5am.∴Temperature risesapproximately(1/4)×10 = 2.5oFin this time.So final temperature isapproximately42 + 2.5 = 44.5oF.Approximatelybecause instantaneous rate of change is 10 at 5ambut thismay change. Maybe by 5:10am temperature is increasing at a rate of 11oFper hour.Answer is(initial temperature)+(rise in temperature)(rise in temperature)≈(time taken)×(rate of change)rate of change=derivativef (5)=10changeinputΔxoutputchanges10Δx