Question

The first and second derivatives of a quadratic Polynomial at x = 1 are 1 and 2 respectively. Then the value of f(1) – f(0) Is given by?

(a) ^3⁄2

(b) ^1⁄2

(c) 1

(d) 0

I got this question by my college director while I was bunking the class.

This intriguing question comes from The nth Derivative of Some Elementary Functions topic in portion Differential Calculus of Engineering Mathematics

Answer 1

Correct choice is (d) 0

The explanation: Let the quadratic polynomial be

f(x) = ax^2 + bx + c

The first derivative at x = 1 is given by

2a + b = 1

Now consider the second derivative at x = 1 which is given by

2a = 2

Solving for the coefficients using equations, we get the values as a = 1 and b = -1

Putting these values back in the polynomial yields

f(x) = x^2 – x + c

Now the required value can be computed as

f(1) – f(0) = (1^2 – 1 + c) – (0^2 – 0 + c)

= (0 + c) – (0 + c) = 0.