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?
- 0
- 1
- 1/2
- None of these
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
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