For s(t)=t³−6t²+9t, find v(t).
Generalize, analyze an edge case, or defend the result without relying on technology.
Unit 07 · Extended Pathway
Contextual Applications of Derivatives
How do derivatives describe motion, related quantities, sensitivity, and local approximation in authentic contexts?
Khaemenes Academy · Calculus I
Extended Practice
Contextual Applications of Derivatives · Show reasoning, notation, intervals, units, and corrections.
Name
Date
What is speed when v=−7 m/s?
Generalize, analyze an edge case, or defend the result without relying on technology.
Can C'(5)>0 while C(5)<0?
Generalize, analyze an edge case, or defend the result without relying on technology.
How can contextual reasonableness be checked?
Generalize, analyze an edge case, or defend the result without relying on technology.
Why substitute measurements after differentiating?
Generalize, analyze an edge case, or defend the result without relying on technology.
A sphere's radius grows at 1 cm/s. Find dV/dt when r=2 cm.
Generalize, analyze an edge case, or defend the result without relying on technology.
What role does a diagram play?
Generalize, analyze an edge case, or defend the result without relying on technology.
If f is concave down near a, does its tangent line generally over- or underestimate?
Generalize, analyze an edge case, or defend the result without relying on technology.
Find the linearization of f(x)=√x at a=4.
Generalize, analyze an edge case, or defend the result without relying on technology.
Why choose a convenient center?
Generalize, analyze an edge case, or defend the result without relying on technology.
Can C'(5)>0 while C(5)<0?
Generalize, analyze an edge case, or defend the result without relying on technology.
How can contextual reasonableness be checked?
Generalize, analyze an edge case, or defend the result without relying on technology.