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Precalculus Mathematics Homework Help
Estimating the Gradient of a Graph: Student's Attempt
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[QUOTE="chwala, post: 6825122, member: 287397"] [B]Homework Statement:[/B] Draw the tangent to the curve at the point where ##x=1##. Use this tangent to claculate an estimate to the gradient of ##y=2^x## when ##x=1## [B]Relevant Equations:[/B] gradient Ok this is a question that i am currently marking...the sketch is here; [ATTACH type="full" alt="1669462338489.png"]317747[/ATTACH] In my mark scheme i have points ##(1,2)## and ##(3,5)## which can be easily picked from the graph to realize an estimate of ##m=1.5## where ##m## is the gradient ...of course i have given a range i.e ##1.6≥m≥1.2## Now to my question. hmmmmm :wink: A student picked the points ##(1,2)## and ##(0.9,1.8)## getting ##m=2## ...the difference from actual is quite big...but the points are picked from their straight line...am i missing something here... Actual gradient using differentiation would be given by; ##\dfrac{dy}{dx}= 2^x\ln 2## ##\dfrac{dy}{dx}[x=1]= 2^1\ln 2=1.386## Your insight welcome. [/QUOTE]
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Precalculus Mathematics Homework Help
Estimating the Gradient of a Graph: Student's Attempt
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