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The maximum height of the road which is made in such a way that the center of the road is higher off the ground than the sides of the road is 16 feet.
<h3>What is the maxima of parabola?</h3>The maxima of a parabola is where, it opens down its vertex at the maximum point in a coordinate graph. By equating the derivative of equation of parabola equal to zero, it can be found out.
A road is made in such a way that the center of the road is higher off the ground than the sides of the road, in order to allow rainwater to drain.
A cross-section of the road can be represented on a graph using the function,
Here,<em> x </em>represents the distance from the center of the road, in feet.
This equation can be written as,
Now to find the maximum height, find the derivative of the above function as,
Equate the above equation to zero as,
Thus, the maximum height of the road which is made in such a way that the center of the road is higher off the ground than the sides of the road is 16 feet.
Learn more about the maxima of parabola here;