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Sagot :
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.
What is the maxima of parabola?
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,
[tex]f(x) = (x - 16)(x+ 16),[/tex]
Here, x represents the distance from the center of the road, in feet.
This equation can be written as,
[tex]f(x) = (x - 16)^2[/tex]
Now to find the maximum height, find the derivative of the above function as,
[tex]f(x) = (x - 16)^2\\f'(x) = (x - 16)^2\\f'(x)=2(x-16)(1)\\f'(x)=2(x-16)[/tex]
Equate the above equation to zero as,
[tex]0=2(x-16)\\0=x-16\\x=16[/tex]
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;
https://brainly.com/question/5399857
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