Science:Math Exam Resources/Courses/MATH104/December 2011/Question 01 (d)
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Question 01 (d)
Find the equation of the tangent line to
at the point corresponding to x = 0.
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!
In order to find the equation of any line (including a tangent), you need to know the slope of the line and the coordinates of a point on the line.
How can you find the slope of a tangent line? What is the point on (and thus the tangent line as well) at ?
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The following solution makes use of the product rule, rather than the quotient rule, for differentiation. Writing the given function as:
allows us to apply the product rule when taking the derivative:
At x = 0, the derivative of y is equal to
The general "point-slope form" for the equation of a straight line is
where (x1,y1) is a point on the line with slope m. We choose x1 = 0 and hence y1 = y(0) = 3. Plugging in these values yields
Therefore, the required equation is y = -5x +3.