Question

What will be the average rate of change of the function [y = 16 – x^2] between x = 3 and x = 4?

(a) 7

(b) -7

(c) 9

(d) -9

The question was asked during an interview for a job.

Enquiry is from Application of Derivative topic in section Application of Derivatives of Mathematics – Class 12

Answer 1

Right choice is (b) -7

To elaborate: Let, y = f(x) = 16 – x^2

If x changes from 3 to 4, then, δx = 4 – 3 = 1

Again f(4) = 16 – 4^2 = 0

And f(3) = 16 – 3^2 = 7

Therefore, δy = f(4) – f(3) = 0 – 7 = -7

Hence, the average rate of change of the function between x = 3 and x = 4 is:

δy/δx = -7/1 = -7.