Given that 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 f(x) = (x – 16)(x + 16), where x represents the distance from the center of the road, in feet.
The height of the road i.e. f(x) is dependent on x, the distance from centre
To find the maximum height of road, let us use derivative tes
f'(x) = (x-16)1+(x+16) (using product rule)
Since second derivative is positive, we have a minimum at x=0
There is no local maximum for the road
But x cannot take values less than 16. Hence x lies after 16 only.
The value of funciton f(x) = (x – 16)(x + 16)
can have minimum when x=16 and maximum when x =infinity