perplexus.info :: Just Math : Minimum of a Real Valued Function

Minimum of a Real Valued Function (Posted on 2024-07-10)

Given:
f(x) = √(x^2-10x+314) + √(x^2+20x+325)

Determine the minimum value of |f(x)| for a real number x.

*** Adapted from a problem appearing in 2017 Singapore M.O. open.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

The required minimum sum is √1249 =~ 35.341.
For an explanation, refer to:
The solution submitted by Larry in this location.
The geometric solution submitted by Brian Smith in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Geometric solution	Brian Smith	2024-07-11 22:07:03
Solution	Larry	2024-07-10 23:59:43

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