Emily, a park ranger, is allowed to use half of a lake for a canoe race. She divides this part of the lake into 6 equal lanes for the canoe racers. What fraction of the lake does each lane represent?

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  1/12

Step-by-step explanation:

1/6 of 1/2 is ...

Each lane represents 1/12 of the lake.

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.