Chebyshev on a Parabola

★ 8/10functions Extrema Absolute Value inequality

Problem

Let $f(x) = x^2$ for $0 \leqslant x \leqslant 1$ , and let $H(a, b)$ be the maximum distance from a point of the graph of $f$ to the line $y = ax + b$ . Find the minimum value of $H(a, b)$ over all lines.

Answer

Solution

Difficulty	8/10
Topics	functions, Extrema, Absolute Value, inequality

Whiteboard

Your sketch is saved only in this browser. To share it, export your drawing as an image (whiteboard menu → Export as → PNG), then upload that image in the comments below.

Discussion

Ask questions, share alternate solutions, and use LaTeX freely.

0 comments

No comments yet.