Jack has a rectangular piece of land, the area of which is represented by a1 = 9.5l. His brother has a different rectangular piece of land, the area of which is represented by a2 = l(14 − l). Let a represent the area in square meters and l represent the length in meters of the pieces of land. The two equations plotted on a graph meet at a point as shown in the image. The area of the brothers’ pieces of land will be the same when the length is meters.

range is infinite on both x and y axis positive and negative

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.

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