Question

Students derive a function to model the results of their experiment on the effect of heat on a chemical where x represents the number of minutes heat was applied. Their (derived) function was m(x)=15x/x^2+2. The teacher said the (actual) function should have been n(x)=12x/x^2+1. For what values of x is their derive function more than the actual function?

Answer 1

Assuming the usual carelessness with parentheses, you just need to solve

15x/(x^2+2) > 12x/(x^2+1)
15x(x^2+1) > 12x(x^2+2)
15x^3 + 15x > 12x^3 + 24x
3x^3 - 9x > 0
3x(x^2-3) > 0
since x>0, that means that
x^2-3 > 0
x > √3