AP Calculus BC Cha 3 E Interpret Related Rates in Applied Contexts Questions

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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AP Calculus BC Cha 3 E Interpret Related Rates in Applied Contexts Questions question 1