3x^2 and 3x^3 are both increasing and positive for x0. How many times greater is the rate of increase of 3x^3 than the rate of increase of 3x^2 at x=4?

Question

3x^2 and 3x^3 are both increasing and positive for x>0. How many times greater is the rate of increase of 3x^3 than the rate of increase of 3x^2 at x=4?

Reiny · Answer

y1 = 3x^2 and y2 = 3x^3 at x=4 dy1/dx = 6x or 24 dy2/dx = 9x^2 = 144 so how many times greater ?

Bekah · Answer

144/24 = 6