For s(t)=t³−6t²+9t, find v(t).
Show a complete solution and verify with a second representation.
Unit 07 · Core Pathway
Contextual Applications of Derivatives
How do derivatives describe motion, related quantities, sensitivity, and local approximation in authentic contexts?
Khaemenes Academy · Calculus I
Core Practice
Contextual Applications of Derivatives · Show reasoning, notation, intervals, units, and corrections.
Name
Date
If v<0 and a<0, is speed increasing or decreasing?
Show a complete solution and verify with a second representation.
Explain the units of acceleration.
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Estimate f'(3) from f(2.9)=7.8 and f(3.1)=8.6.
Show a complete solution and verify with a second representation.
How can contextual reasonableness be checked?
Show a complete solution and verify with a second representation.
Differentiate x²+y²=100 with respect to time.
Show a complete solution and verify with a second representation.
What role does a diagram play?
Show a complete solution and verify with a second representation.
A sphere's radius grows at 1 cm/s. Find dV/dt when r=2 cm.
Show a complete solution and verify with a second representation.
What role does a diagram play?
Show a complete solution and verify with a second representation.
Use that linearization to estimate √4.1.
Show a complete solution and verify with a second representation.
Write the differential relation.
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Find the linearization of f(x)=√x at a=4.
Show a complete solution and verify with a second representation.
Write the differential relation.
Show a complete solution and verify with a second representation.
Interpret C'(5)=12 when C is dollars and x is units produced.
Show a complete solution and verify with a second representation.
Estimate f'(3) from f(2.9)=7.8 and f(3.1)=8.6.
Show a complete solution and verify with a second representation.
How can contextual reasonableness be checked?
Show a complete solution and verify with a second representation.