(Optimization) - Finding the Minimal Distance between a Point and a Parabola

In this video, we solve an optimization problem of finding a point on a parabola that is the closest to a fixed point off of the curve.

This lecture is based upon Section 4.7 of Calculus by James Stewart. Please post any questions you might have below in the comment field and Dr. Misseldine (or other commenters) can answer them for you. Please also subscribe for further updates.

[xddpfyg]

This is a phenomenal video, and the explanation make sense. Don't know why this doesn't have more views

[scottekoontz]

This can also be solved using a similar method to the "distance from point to line" problems. You have a point, get the slope. The slope of the parabola changes with values of x (or y) but you can still get the formula for the lines that can be made from the point to the parabola. The only calc needed is the first derivative for the slope of a parabola.

E.g., x = (y^2)/2 means x' = y, so perp line will have slope dx/dy of -1/y.

Point-slope formula: (x - 1) = -1/y (y - 4), thus x = 4/y (multiple points)

We have two equations, set the x values equal to each other: 4/y = (y^2)/2, thus y^3 = 8, etc.

[TheFnut]

This is great! Would love to see a version of this in code, can't find that anywhere.

[patheticotaku]

Wow!!! Understood the concept thanks professor 😍

[abhiacharya]

Thanks a lot sir, It's now cristal clear

[berrybby]

i got finals in 2 hours and its 6am thank you so much