Jack wants to bike from his house to jill's house, which is located three blocks east and two blocks north of jack's house. after biking each block, jack can continue either east or north, but he needs to avoid a dangerous intersection one block east and one block north of his house. in how many ways can he reach jill's house by biking a total of five blocks?

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.