The graph of the function f(x) = (x - 3)(x + 1) is shown.

the second one

Step-by-step explanation:

y is postitive when x <  -1 and x > 3, but y is decreasing only when x < 1 so the case where both are true is when x < -1   option 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.