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

Multiple Choice

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 $y=3\left(x^{3}-12 x^{2}+48 x+36\right)$ .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.Which of the following is a good estimate of the elevation after 7.5 horizontal miles.(You do not know the shape of the path explicitly after 7 miles!)

A) 381 feet
B) 394.5 feet
C) 408 feet
D) 421.5 feet