Suppose that y varies inversely with x. use the information to find k, and then choose the equation of variation. x=2 when y=2

see explanation

Step-by-step explanation:

Given that y varies inversely as x then the equation relating them is

y = ← k is the constant of variation

To find k use the condition

x = 2 when y = 2

k = yx = 2 × 2 = 4, hence

y = ← equation of variation

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.