AP Calculus BC Flashcards: Approximating Values of a Function Using Local Linearity and Linearization
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 10 cards to help you master important concepts.
What is the graphical interpretation of a locally linear approximation?
Graphically, it is the tangent line to the function at the point being used for the approximation.
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What is the graphical interpretation of a locally linear approximation?
Graphically, it is the tangent line to the function at the point being used for the approximation.
Why is a tangent line a suitable tool for approximating function values?
The tangent line is the graph of a locally linear approximation, meaning it closely models the function's behavior near the point of tangency.
What is the primary method for approximating a value on a curve using local linearity?
To approximate a value on a curve, you use the equation of the tangent line to the function at a nearby, known point.
What determines if a tangent line approximation is an overestimate or an underestimate?
The behavior of the function's curve near the point of tangency, specifically its concavity, determines if the approximation is an overestimate or underestimate.
If a function is concave up at the point of tangency, will the tangent line approximation be an overestimate or an underestimate?
The approximation will be an underestimate because the tangent line lies below the function's curve.
What is a tangent line approximation?
It is the process of using the y-value on a tangent line at a certain x to estimate the corresponding y-value on the original function's curve.
If a function is concave down at the point of tangency, what is the relationship between the tangent line value and the actual function value?
The tangent line value will be an overestimate of the actual function value because the tangent line lies above the curve.
What is a locally linear approximation?
It is an approximation of a function's value using its tangent line, which is accurate near the point of tangency.
When does the accuracy of a tangent line approximation decrease?
The accuracy of the approximation decreases as the point of approximation moves further away from the point of tangency.
What does it mean for a function to be 'locally linear'?
It means that near a specific point, the graph of the function is so close to its tangent line that the line can be used for approximations.