Science:Math Exam Resources/Courses/MATH110/December 2014/Question 04 (c)

MATH110 December 2014

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Question 04 (c)

The following limit $$\lim _{h\to 0}{\frac {{\frac {1}{(2+h)^{2}}}-{\frac {1}{4}}}{h}}$$ equals the derivative ${\textstyle f'(a)}$ for some function ${\textstyle f}$ and some point ${\textstyle a}$. (c) Confirm your answer to part (b) by computing the derivative ${\textstyle f'(a)}$ for the function ${\textstyle f}$ and point ${\textstyle a}$ you identified in part (a) using appropriate differentiation rules.

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
Use the power rule.

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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 power rule, the derivative of $f$ is $f'(x)=(x^{-2})'=-{\frac {2}{x^{3}}}$. Then, plugging $x=2$, we get $f'(2)=-{\frac {2}{2^{3}}}=\color {blue}-{\frac {1}{4}}$, which matches with the answer to part (b).