# Math Help - optimization - distence/intensity of lamps

1. ## optimization - distence/intensity of lamps

Two lamps are of intensities 40 and 5 candle-power respectively and are 6m apart. If the intensity of the illumination I, at any point is directly proportional to the power of the source and inversely proportional to the square of the distance from the source, find the darkest point on the line joining the two lamps.

im not sure how to work with the proportions.

2. ## Is this a straight line problem?

The 2 distances seem to be x and 6-x. Then the intensity would be:

$
I = \frac{40}{x^2} + \frac{5}{(6-x)^2}
$

3. this is the equation i found as well ...but i cant seem to get the correct answer.

im supposed to find the derivative and equate to zero right?

yes