Optimization calculus problem

  • #1

Homework Statement


The illumination of an object by a light source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source. If two light sources, one three times as strong as the other, are placed 10 feet apart, where should an object be placed on the line between the sources so as to receive the least illumination?


Homework Equations


1/illumination=distance^2 and illumination=strength. 1/3x=y distance=10 so 1/100= illumination??


The Attempt at a Solution


find the derivative of what equation to optimize?
 

Answers and Replies

  • #2
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Let s = strength of a source
Let d = distance from source.

I =ks/d2

The way I read this is that the total illumination an object receives is the sum of the illuminations from the two light sources, so
IT = I1 + I2

From this relationship you should be able to write the total illumination an object at a distance of x feet from the left source gets.

Then differentiate the expression for IT.
 

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