If y varies inversely as x, and y = 3 as x = -2, find y for the x-value of -1.

y = 6

Step-by-step explanation:

For inverse variation

xy = k where k is a constant

3(-2) = k

-6 = k

xy = -6

(-1) y = -6

Divide by -1

y = 6

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.