Set p = {x, 4, 6, 10, -2, x, 6, 1, x} in set p, if the value of x is 4 greater than the largest numerical value present, what is the range of the set?

16.

Step-by-step explanation:

The largest numerical value present in the set P is 10, then x is 4+10 = 14. Then the set P is

P = {14, 4, 6, 10, -2, 14, 6, 1, 14}.

Now, the range is the difference between the greatest and the smallest element in the set. The greatest number is 14 and the smallest is -2, then the range is

14-(-2) = 14+2 = 16.

Then the range of the set P is 16.

answer

the correct answer is

explanation

the given function is

the excluded values are obtained by solving:

we factor to obtain:

the excluded values are

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.