Using first principles, find f'(2) for f(x)=x².
Generalize, analyze an edge case, or defend the result without relying on technology.
Unit 04 · Extended Pathway
The Derivative from First Principles
How does the limiting slope of secant lines define instantaneous change?
Khaemenes Academy · Calculus I
Extended Practice
The Derivative from First Principles · Show reasoning, notation, intervals, units, and corrections.
Name
Date
If position is measured in meters and time in seconds, give velocity units.
Generalize, analyze an edge case, or defend the result without relying on technology.
Write the tangent-line equation to y=x² at x=1.
Generalize, analyze an edge case, or defend the result without relying on technology.
What feature of f often corresponds to a zero of f'?
Generalize, analyze an edge case, or defend the result without relying on technology.
Name a point where |x| is not differentiable.
Generalize, analyze an edge case, or defend the result without relying on technology.
Write the tangent-line equation to y=x² at x=1.
Generalize, analyze an edge case, or defend the result without relying on technology.
If position is measured in meters and time in seconds, give velocity units.
Generalize, analyze an edge case, or defend the result without relying on technology.
What does f'(a)>0 indicate locally?
Generalize, analyze an edge case, or defend the result without relying on technology.
Using first principles, find f'(3) for f(x)=x².
Generalize, analyze an edge case, or defend the result without relying on technology.
If position is measured in meters and time in seconds, give velocity units.
Generalize, analyze an edge case, or defend the result without relying on technology.
Write the tangent-line equation to y=x² at x=1.
Generalize, analyze an edge case, or defend the result without relying on technology.
What feature of f often corresponds to a zero of f'?
Generalize, analyze an edge case, or defend the result without relying on technology.