Question

Item 3

Oil is spilled onto a kitchen floor. The area covered by the oil at time t is given by the function A, where A(t) is measured in square centimeters and t is measured in seconds. Which of the following gives the rate at which the area covered by the oil is changing at time t=10 ?

Answer 1

By an online search, i found that the options are:

Option A. A(10)

Option B. A(11)-A(9)

Option C. A(10)/10

Option D. A’(10)

Let´s start by defining the concept of a derivative.

When we have a function f(x), the derivative, f´(x), is a measure of the rate of change of f(x) with respect to the variable x.

Then if A(t) represents the area covered by the oil, A´(t) is the rate of change of this area as a function of t.

Particularly, A´(10), will be the rate of change at t = 10.

Then the correct option is: Option D. A´(10)