According to the video, what are two interpretations of the derivative of a function at a point?

The derivative of a function at a point is the slope of the tangent line at that point and the rate of change of the function at that point.

Using the limit definition, find the derivative of the function f(x) = 3. Show your work.

f'(x) = lim (h->0) [f(x+h) - f(x)] / h = lim (h->0) [3 - 3] / h = lim (h->0) 0 / h = 0

Explain how the concept of a limit is used to find the derivative of a function.

The derivative is found by taking the limit of the difference quotient as h approaches zero. This represents the slope of the tangent line as the distance between two points on the curve becomes infinitesimally small.

Derivatives Using Limits Lesson Plan for Grade 12

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Learning Objective

I can calculate the derivative of a function using limits.

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).

Derivatives Using Limits

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Learning Objective

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Key Concepts

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