AP Calculus BC 4.5: Related Rates in Context

Practise AP Calculus BC 4.5 questions by relating changing geometric quantities, differentiating with respect to time, and interpreting rates in context.

Exam points

Relate x, y and distance from the origin, then differentiate with respect to time.
Use a cone’s volume–depth relationship to determine the concavity of water depth over time.

[Maximum number: 1]

A point moves along the curve $y=x^{2}+1$ so that the x-coordinate is increasing at the constant rate of $\frac{3}{2}$ units per second. The rate, in units per second, at which the distance from the origin is changing when the point has coordinates (1,2) is equal to

$\frac{7 \sqrt{5}}{10}$

$\frac{3 \sqrt{5}}{2}$

$\frac{3 \sqrt{5}}{5}$

$\frac{5}{2}$

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CHA-3.E—Interpret related rates in applied contexts question 1