Aball is thrown from an initial height of 7 feet with an initial upward velocity of 30ft/s . the ball's height h (in feet) after t seconds is given by the following. h=7+30t-16t^2
find all values of t for which the ball's height is 20 feet.
round your answer(s) to the nearest hundredth.

t = —— seconds

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.