Jack is practicing pitching with his team. He rotates pitching with his teammates after 12 pitches thrown. He has to throw at least 50 strikes before he can leave. How many rotations must Jack at least make if he throws 14 balls?

step-by-step explanation:

b and c

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.

step-by-step explanation: