A missile is launched along a path determined by the function below, where f(x) is the height of the missile in feet x seconds after the launch. A plane is flying nearby at a height of 650 feet.
Is the plane in danger of being hit by the missile?
Why or why not?

f(x)=-2x^2+72x

The plane will be fine.

Step-by-step explanation:

There are no real solutions.

11 feet 6 inches and 8 feet 6 inches

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.