Question

Find the rate of change of its elevation when x=22

Answer 1

To find the rate of change of its elevation we can derive the position function:

`y=-(1)/(110)x^2+127`
`y^(\prime)=(d(y))/(dx)=d(-(1)/(110)x^2+127)/d(x)`
`y^(\prime)=(-1)/(55)x`

The rate of change of its elvation when x=22 is

`(-1)/(55)\cdot22=(-22)/(55)=(-2)/(5)=-0.4`

That represents the slope of the tangent line to the function at x=22.