Find the Closest Point on a Graph to (4,1) →(No Calculus!)
Автор: Mind Leap
Загружено: 2025-10-02
Просмотров: 18
In this video we find the point on the curve y = sqrt(x − 2) + 1 that’s closest to (4,1) using a simple idea: work with distance squared, which turns the problem into a plain quadratic in x. A U-shaped quadratic has a single lowest point, so the vertex gives the minimum distance instantly—no derivatives needed.
What you’ll learn:
How to turn a “shortest distance” problem into a quadratic in x
Why minimizing distance and minimizing distance-squared pick the same x
How the vertex guarantees a global minimum (not just a local one)
A reusable checklist you can apply to other “closest point” problems
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#math #algebra #optimization #precalculus #geometry #MindLeapTutor
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