Derivatives Using Limits
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Objective
I can calculate the derivative of a function using limits.
Part 1 of 4
Warm-up video
Professor Dave Explains · 10:05Vetted channel
We don't generate video — this one is by Professor Dave Explains on YouTube. The practice questions and exit ticket below were drafted by AI for this objective, and every question is editable in the teacher guide.
Part 2 of 4
Key concepts
3 concepts
- 1
The derivative of a function tells us about the rate of change in that function at a particular input value.
- 2
The slope of the secant line is rise over run, or f(x) minus f(a) over x minus A; the slope of the tangent line will be the slope of this secant line in the limit of x approaching A.
- 3
The power rule states that the derivative of xⁿ is equal to n times x^(n-1).
Part 3 of 4
Practice
4 questions
According to the video, what are two interpretations of the derivative of a function at a point?
If a function is decreasing at a particular point, what can be said about the value of its derivative at that point?
Part 4 of 4
Exit ticket
Quick comprehension check
“Use limits to find the derivative of f(x) = 3x² + 2x. Show all steps.”
Sample answer included in the free materials
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