AP Calculus AB 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 does a tangent line represent in the context of function approximation?
The tangent line is the graph of a locally linear approximation of the function, providing estimated values for the function near the point of tangency.
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What does a tangent line represent in the context of function approximation?
The tangent line is the graph of a locally linear approximation of the function, providing estimated values for the function near the point of tangency.
What is a tangent line approximation (or linearization)?
It is the process of using the y-value from a function's tangent line equation to estimate the actual y-value of the function at a nearby point.
Why is a tangent line approximation only accurate 'near the point of tangency'?
The approximation's accuracy decreases as the distance from the point of tangency increases because the curve diverges from the straight path of the tangent line.
What is another term for the tangent line used as an approximation?
The tangent line used for approximation is also known as the locally linear approximation or the linearization of the function.
If a function is concave down at the point of tangency, is the tangent line approximation an overestimate or an underestimate?
The tangent line will lie above the curve, resulting in an overestimate of the actual function value.
How do you perform a tangent line approximation for f(c) given a known point (a, f(a))?
First, find the equation of the tangent line at x=a, then substitute x=c into that line's equation to find the approximate value.
What is local linearity?
Local linearity is the concept that a differentiable function's graph closely resembles its tangent line near the point of tangency.
What determines if a tangent line approximation is an overestimate or an underestimate?
The function's behavior, specifically its concavity, near the point of tangency determines whether the approximation is an overestimate or an underestimate.
What is the primary tool used to approximate a value on a curve near a known point?
The equation of the tangent line at the known point is used to approximate values on the curve for nearby points.
If a function is concave up at the point of tangency, is the tangent line approximation an overestimate or an underestimate?
The tangent line will lie below the curve, resulting in an underestimate of the actual function value.