Science:Math Exam Resources/Courses/MATH110/April 2018/Question 01 (a)/Solution 1

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 ${\textstyle {\color {blue}(c),(e)}}$.