Answer
The value of x at the lowest point on the graph is 45. The minimum value of y using the given equation is 190.
Work Step by Step
Consider the given graph. The lowest point of the curve drawn using the function f occurs at the point 45 of the x-axis.
Consider the given function:
$f\left( x \right)=0.4{{x}^{2}}-36x+1000$
Substitute the value of x as 45 in the above equation.
$\begin{align}
& f\left( 45 \right)=0.4{{\left( 45 \right)}^{2}}-36\left( 45 \right)+1000 \\
& =810-1620+1000 \\
& =190
\end{align}$
Here, the coordinate of the point on the graph f is$\left( 45,190 \right)$. It indicates that if the age of the driver is 45 then thenumber of the accidents is 190 per 50 million miles. This point shows the minimum number of accidents.
