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?

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?

Explanation

Let the quadratic polynomial be f(x) = ax^2 + bx + c.

Given that f'(1) = 1 and f''(1) = 2.

f'(x) = 2ax + b

f''(x) = 2a

f'(1) = 1 => 2a + b = 1

f''(1) = 2 => 2a = 2 => a = 1

Substituting a = 1 in the first equation, we get:

2 + b = 1 => b = -1

Now, f(x) = x^2 - x + c

f(1) = 1^2 - 1 + c = c

f(0) = 0^2 - 0 + c = c

f(1) - f(0) = c - c = 0