Question

What will be the increment of the differentiable function f(x) = 2x^2 – 3x + 2 when x changes from 3.02 to 3?

(a) 0.18

(b) 0.018

(c) 0.16

(d) 0.016

This question was addressed to me in an interview for internship.

Question is taken from Application of Derivative for Error Determination in portion Application of Derivatives of Mathematics – Class 12

Answer 1

Right option is (a) 0.18

For explanation I would say: Let, y = f(x) = 2x^2 – 3x + 2

So, f’(x) = 4x – 3

Clearly, as x changes from 3 to 3.02, the increment of x is:

3.02 – 3 = 0.02

So, increment in f(x) = f(3.02) – f(3)

= 2(3.02)^2 – 3(3.02) + 2 – 2(3)^2 – 3(3) + 2

= 0.1808

Now, differential of y is dy

We get, f’(3) * 0.02 = (4.3 – 3)*0.02

= 0.18