A motorist travelled from Ibadan to Lagos a distance of 142km at an average speed of 60km/h. he spent 2 1/2hours in Lagos and then returned to Ibadan at an average speed of 80km/h. At what time did he arrive in Ibadan? What is the average speed of the whole journey?

26

step-by-step explanation:

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.