Question

If, y = 1/(1 + x + x^2 + x^3), then what is the value of y’ at x = 0?

(a) 0

(b) 1

(c) -1

(d) ½

I got this question in an interview for internship.

Enquiry is from First Order Derivative in chapter Limits and Derivatives of Mathematics – Class 11

Answer 1

The correct answer is (c) -1

Easiest explanation: Given, y = 1/(1 + x + x^2 + x^3)

Assuming x ≠ 1

Or, y = (x – 1)/(x – 1)( x^3 + x^2 + x + 1)

Differentiating both the sides with respect to x, we get,

dy/dx = [(x^4 – 1)*1 – (x – 1)*4x^3]/ (x^4 – 1)^2

Thus, putting x = 0 in the above equation, we get,

(dy/dx) = -1/(-1)^2

= -1