Using first principles, find f'(2) for f(x)=x².
Show a complete solution and verify with a second representation.
Unit 04 · Core Pathway
The Derivative from First Principles
How does the limiting slope of secant lines define instantaneous change?
Khaemenes Academy · Calculus I
Core Practice
The Derivative from First Principles · Show reasoning, notation, intervals, units, and corrections.
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Name a point where |x| is not differentiable.
Show a complete solution and verify with a second representation.
What feature of f often corresponds to a zero of f'?
Show a complete solution and verify with a second representation.
What does f'(a)>0 indicate locally?
Show a complete solution and verify with a second representation.
What feature of f often corresponds to a zero of f'?
Show a complete solution and verify with a second representation.
What does f'(a)>0 indicate locally?
Show a complete solution and verify with a second representation.
If position is measured in meters and time in seconds, give velocity units.
Show a complete solution and verify with a second representation.
Write the tangent-line equation to y=x² at x=1.
Show a complete solution and verify with a second representation.
If position is measured in meters and time in seconds, give velocity units.
Show a complete solution and verify with a second representation.
Write the tangent-line equation to y=x² at x=1.
Show a complete solution and verify with a second representation.
Name a point where |x| is not differentiable.
Show a complete solution and verify with a second representation.
Using first principles, find f'(3) for f(x)=x².
Show a complete solution and verify with a second representation.
Name a point where |x| is not differentiable.
Show a complete solution and verify with a second representation.
Using first principles, find f'(4) for f(x)=x².
Show a complete solution and verify with a second representation.
What does f'(a)>0 indicate locally?
Show a complete solution and verify with a second representation.
What feature of f often corresponds to a zero of f'?
Show a complete solution and verify with a second representation.