Math CentralQuandaries & Queries


Question from Victoria, a student:

The flight path of a bumblebee above the ground can be modelled by the function f(x)= 2x^3- 17x^2+ 11x + 130. Where x is the time in seconds and f(x) represents the height in inches above the ground. The entrance to the bee's hive is located 100 inches above the ground. Determine when the bumblebee's height is greater than 100 inches. The bee's height was monitored from 0 to 25 seconds inclusive. (over the domain 0 <or equal to x <or equal to 15)

Hi Victoria,

I can help get you started.

To solve $f(x) > 100$ you should first solve $f(x) = 100.$ Simplifying this expression gives

\[2 x^3 - 17 x^2 + 11 x + 30 = 0\]

I don't see any obvious factorization of the left side so I used the Factor Theorem.

Try it and write back if you need more help,


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