One Fine Day You Take a Hike Up a Mountain $y=5\left(x^{3}-12 x^{2}+48 x+36\right)$

One fine day you take a hike up a mountain path.Using your trusty map you have determined that the path is approximately in the shape of the curve $y=5\left(x^{3}-12 x^{2}+48 x+36\right)$ .Here y is the elevation in feet above sea level and x is the horizontal distance in miles you have traveled, but your map only shows the path for 7 miles, horizontal distance.If your friend, who is not in "good shape" followed this path for 15 miles total, in horizontal distance, the day before, it makes sense that the equation for the elevation continues to hold much beyond the 7 mile mark.