Science:Math Exam Resources/Courses/MATH110/December 2017/Question 01 (b)

MATH110 December 2017

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Question 01 (b)
Find the equation of the tangent line to the graph of ${\textstyle y=f(x)}$ at ${\textstyle x=1}$ given that ${\textstyle f(1)=2}$ and ${\textstyle f'(1)=3}$.

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
Recall that, for a function ${\textstyle y=f(x)}$, the equation of tangent line at the point ${\textstyle x=a}$ is given by ${\textstyle y=f(a)+f'(a)(x-a)}$.

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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. By the Hint, we need to put ${\textstyle a=1}$ and use the values ${\textstyle f(1)}$ and ${\textstyle f'(1)}$ which are given. Recall that the equation of tangent line at the point ${\textstyle x=1}$ is $$y=f(1)+f'(1)(x-1).$$ Since ${\textstyle f(1)=2}$ and ${\textstyle f'(1)=3}$, the equation becomes $$y=2+3(x-1).$$ Alternatively, this can be expanded and simplified as $$y=3x-1.$$ Answer: the equation of tangent line is ${\textstyle {\color {blue}y=3x-1}}$.