Given the graph of f '(x), the derivative of f(x), which of the following statements are true about the graph of f(x)? (4 points) 2.
Given the graph of f '(x), the derivative of f(x), which of the following statements are true about the graph of f(x)?

Graph is parabola with x intercepts at x equals 0 and 3 and vertex at x = 1

I. The graph of f is decreasing on the interval (0, 2).
II. The graph of f is increasing on the interval (1, infinity).
III. The graph of f has point of inflection at x = 0.

a I only
b II only
c III only
d None of these are true

(I) is true, since the plot shows f'(x) is negative on (0, 2)

(II) is false, since f'(x) is negative on (1, 2), so f(x) is decreasing over this interval

(III) is false. An inflection point can only occur at a point x if f''(x) is zero or doesn't exist. But at x = 0, the tangent line to f'(x) clearly has a negative, non-zero slope.

This makes A the correct choice.

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.