The graph of g(x) = x – 8 is a transformation of the graph of f(x) = x. Which of the following describes the transformation?
(A) translation 8 units down
(B) translation 8 units up
(C) translation 8 units right
(D) translation 8 units left

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.

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.