Science:Math Exam Resources/Courses/MATH104/December 2010/Question 01 (h)

MATH104 December 2010

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Question 01 (h)
Find the equation of the tangent line to the graph of $y=x\ln x$ at x = 1.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
What are two critical pieces of information to find the equation of a line?

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. This requires us to find a point on the line and its slope. When $x=1$, $x\ln x=1\cdot 0=0$ so we know the point $(1,0)$ is on the line. If $y=x\ln x$ then ${\frac {dy}{dx}}=(x\ln x)'=\ln x+x\cdot {\frac {1}{x}}=\ln x+1$ and ${\frac {dy}{dx}}{\bigg |}_{x=1}=1$ so the slope of the line is $1$. The equation of the tangent line is then $y-0=1(x-1)$, by the point-slope formula, or $\color {blue}y=x-1$.

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