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?
Answer: 0
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
This question appeared in
Past Papers (4 times)
Lecturer Mathematics Past Papers and Syllabus (1 times)
SPSC 25 Years Past Papers Subject Wise (Solved) (2 times)
SPSC Past Papers (1 times)
This question appeared in
Subjects (1 times)
MATHS MCQS (1 times)
Related MCQs
- When a quadratic polynomial is divided by x−2, we are left with _____?
- HCF and LCM of two polynomials are x - 2 and x³ + 3x² - 6x - 8 respectively. If one polynomial is x² - x - 2, find the second polynomial?
- If H.C.F and L.C.M of two polynomials are x - 3 and x³ - 9x² + 26x - 24 respectively. Find the second polynomial when polynomial is x² - 5x - 6?
- Under Galois theory, the roots of a polynomial is solvable by radicals if and only if the polynomial’s Galois group is?
- If the sum and product of the roots of a quadratic equation are 55 and 66 respectively, which of the following represents the correct quadratic equation?
- Following are derivatives of the Ectoderm except:
- Derivatives of the Müllerian duct include all except:
- The pronoun "he" and its derivatives are used of any person whether male or female
- If the roots of a quadratic equation are 1 + √5 and 1 - √5. The quadratic equation is?
- One zero of the polynomial p(x) = x² - 4x + 3 is?
