6 min read
This study guide covers approximating function values using local linearity and tangent lines. It explains how to find the equation of a tangent line and use it for approximation. The guide also discusses how a function's concavity determines whether the approximation is an overestimate or underestimate, and provides worked examples and practice questions. Key terms include local linearity, tangent, concavity, overestimate, and underestimate.
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Question 1 of 10
Zooming in on a function's graph at a point makes it look like a straight line! 🤩 This is the idea behind local linearity. Where is the tangent line approximation most accurate?
Far away from the point of tangency
At the y-intercept
Close to the point of tangency
Where the function's second derivative is zero