Question

Explain the difference between the average rate of change of y as x changes from a to b, and the instantaneous rate of change ofy at x=a.

A. The average rate of change of y as x changes from a to b can be found using the formula ​, where y​f(x). The instantaneous rate of change of y at xa is found by taking the limit as b approaches a of the stated formula.
B. The average rate of change of y as x changes from a to b can be found by using the formula ​, where y​f(x). The instantaneous rate of change of y at xa is found by taking the limit as b approaches a of the stated formula.
C. The instantaneous rate of change of y at xa can be found by using the formula ​, where y​f(x). The average rate of change of y as x changes from a to b is found by taking the limit as b approaches a of the stated formula.
D. The instantaneous rate of change of y at xa can be found using the formula ​, where y​f(x). The average rate of change of y as x changes from a to b is found by taking the limit as b approaches a of the stated formula.

Answer 1

The given options are not clear enough, so i have attached the full question with the correct options.

Answer:

Option A:

Average rate of change=[f(b) - f(a)]/(b-a)

Instantaneous rate of change of y at x = a is found by finding the limit as "b" approaches "a"

Explanation:

The average rate of change of a function f(x) on an interval [a, b] is defined as the slope of the secant line, which is calculated by the formula;

[f(b) - f(a)]/(b - a)

While the instantaneous rate of change of f(x) at x = a is defined as the slope of the tangent line, which is calculated by finding the limit as "b" approaches "a". This is written as; f'(a) .

Looking at the options, the correct answer is option A.