Directions: For the following systems, determine whether or not the ordered triple (1, -1, -2) is a solution to the equations below. 1. 3x – 3y – z = 2

Step-by-step explanation:

Put x = 1, y = -1 and z = -2 to the equation 3x - 3y - z = 2, and check the equality:

3(1) - 3(-1) - (-2) = 3 + 3 + 2 = 8 ≠ 2

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.