What is the graph?
A) positive slope
B) negative slope
C)m=0.
D) undefined slope

Positive Slope.

Negative Slope would be another way arond.

m = 0 will become a constant graph or a horizontal line.

undefined slope is basically a vertical line.

So the answer is positive slope.

Positive Slope

Step-by-step explanation:

You know it's a positive slope because from the left to right, this line is ascending. Remember: You always have to check from left to right, not right to left!

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

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.