Related rates of change
Practice Flashcards
Flip to reveal answersWhat is the chain-rule link in a related-rates problem (V depending on r)?
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All 8 Flashcards — Related rates of change
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Question
What is the chain-rule link in a related-rates problem (V depending on r)?
Answer
dV/dt = dV/dr · dr/dt.
Question
What are the three steps of a related-rates problem?
Answer
1) Write the formula linking the quantities. 2) Differentiate w.r.t. time t. 3) Substitute the known rate and value, then solve.
Question
Which formula links the base and height of a sliding ladder?
Answer
Pythagoras: x² + y² = L² (L the fixed ladder length).
Question
What does a negative rate of change mean?
Answer
The quantity is decreasing (e.g. the top of a ladder sliding down, or a tank draining).
Question
Sphere: dV/dr = ? (V = (4/3)πr³)
Answer
dV/dr = 4πr² (the surface area).
Question
For a cone with r = h/2, how do you simplify V = (1/3)πr²h before differentiating?
Answer
Substitute r = h/2 to get V = (1/3)π(h/2)²h = πh³/12, a function of h only.
Question
d/dx of arctan(u)?
Answer
u′/(1 + u²).
Question
When should you substitute the given numbers in a related-rates problem?
Answer
Last — differentiate the general formula first, then substitute the rate and value at that instant.
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Full study notes for Related rates of change
Topic 5.14 hub
Implicit & related rates (HL only)
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