Science:Math Exam Resources/Courses/MATH110/December 2015/Question 04 (a)

MATH110 December 2015

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Question 04 (a)
Consider a curve $y={\frac {1}{3x}}.$ (a) Write down an expression for ${\frac {dy}{dx}}{\bigg |}_{x=2}$ using the definition of derivative as a limit. Answers that do not involve the limit definition of derivative will receive no marks.

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 given function $f$, its derivative at a point $a$ is defined by $f'(a)=\lim _{h\to 0}{\frac {f(a+h)-f(a)}{h}}$

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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. Let $f(x)={\frac {1}{3x}}$. By the definition of derivative, we have ${\begin{aligned}{\frac {dy}{dx}}{\bigg |}_{x=2}=f'(2)=\lim _{h\to 0}{\frac {f(2+h)-f(2)}{h}}=\color {blue}\lim _{h\to 0}{\frac {{\frac {1}{6+3h}}-{\frac {1}{6}}}{h}}\end{aligned}}$