Science:Math Exam Resources/Courses/MATH110/April 2018/Question 01 (a)

MATH110 April 2018

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Question 01 (a)
Select all that apply: The rate of the function ${\textstyle f(x)}$ at ${\textstyle x=3}$ is given by (a) ${\textstyle f(3)}$ . (b) ${\textstyle {\frac {f(3)-f(2)}{3-2}}}$ . (c) ${\textstyle f'(3)}$ . (d) the slope of the secant line through the points ${\textstyle (3,f(3))}$ and ${\textstyle (2,f(2))}$ . (e) the slope of the tangent line through the point ${\textstyle (3,f(3))}$ .

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
The rate of change at a point is the instantaneous rate of change.

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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. The rate of change of a function at a point is the value of the derivative of the function at that point. Statement (a) is simply the value of ${\textstyle f}$ at ${\textstyle x=3}$ , not the value of the derivative. Statements (b) and (d) both give the average rate of change of ${\textstyle f}$ between ${\textstyle x=2}$ and ${\textstyle x=3}$ , whereas the question asks for the instantaneous rate of change at ${\textstyle x=3}$ . Statements (c) and (e) both give the value of the derivative of ${\textstyle x=3}$ , which is what we are after. Answer: The correct answers are ${\textstyle {\color {blue}(c),(e)}}$ .