# Science:Math Exam Resources/Courses/MATH102/December 2017/Question 10 (b)

MATH102 December 2017
Other MATH102 Exams

### Question 10 (b)

An animal foraging in a food patch has a net energy gain of ${\textstyle f(t)}$ by the time it has been foraging for ${\textstyle t}$ min (where ${\textstyle t}$ is nonnegative and ${\textstyle f(0)=0}$).

(b) For any positive time ${\textstyle t}$, what is the geometric interpretation of the function ${\textstyle A(t)}$, as it appears on the graph of ${\textstyle f(t)}$?
Circle the letter corresponding to your choice.

A. It is the slope of the secant line from ${\textstyle (0,0)}$ to ${\textstyle (t,f(t))}$.

B. It is the slope of the tangent line at ${\textstyle (t,f(t))}$.

C. It is the tangent line to ${\textstyle f(t)}$ that goes through the origin.

D. It is the steepest secant line on ${\textstyle f(t)}$.

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