Question

part c only (by differentiation, show that the mode of X is 2.5​

Answer 1

Answer:

• To earn the first point the response must provide both a difference and a quotient and must explicitly

use values of f from the table.

• Simplification of the numerical value is not required to earn the first point. If the numerical value is

simplified, it must be correct.

• The interpretation requires all of the following: distance r = 2.25, density of bacteria (population)

is increasing or changing, at a rate of 8, and units of milligrams per square centimeter per

centimeter.

• The second point (interpretation) cannot be earned without a nonzero presented value for f ′(2.25 .)

• To earn the second point the interpretation must be consistent with the presented nonzero value for

f ′(2.25 .) In particular, if the presented value for f ′(2.25) is negative, the interpretation must

include “decreasing at a rate of f ′(2.25) ” or “changing at a rate of f ′(2.25 .) ” The second point

cannot be earned for an incorrect statement such as “the bacteria density is decreasing at a rate of

−8 … ” even for a presented f ′(2.25 8. ) = −

• The units ( 2 mg/cm /cm ) may be attached to the estimate of f ′(2.25) and, if so, do not need to be

repeated in the interpretation.

• If units attached to the estimate do not agreeStep-by-step explanation: