Derivative help

[lightnsweet]

I'm not sure where to start with this, I have to use derivatives to solve this problem.


Two particles move on a straight line. Their positions are measured from a
fixed point on the line, in nanometers. The position of particle A after t seconds
is given by the formula 10 + 3t. The position of particle B is given by 15 + t^2.


Write down an expression for the distance between the two particles. How
far apart are they at the start of the experiment?
A chemical reaction occurs if the particles come within 3 nanometers of each
other. Do you expect this reaction to occur?

Thank You!

 

[JeffM]

I'm not sure where to start with this, I have to use derivatives to solve this problem.


Two particles move on a straight line. Their positions are measured from a
fixed point on the line, in nanometers. The position of particle A after t seconds
is given by the formula 10 + 3t. The position of particle B is given by 15 + t^2.


Write down an expression for the distance between the two particles. How
far apart are they at the start of the experiment?
A chemical reaction occurs if the particles come within 3 nanometers of each
other. Do you expect this reaction to occur?

Thank You!

Hint 1: What is the minimum distance separating the two particles? Is it greater than 3? Minima and maxima problems are frequently solved using derivatives, no?

Hint 2: What is the first step in finding a minimum or maximum using derivatives?

 

[HallsofIvy]

The distance between points A and B, on a line, is |A- B|.