The expression ax2 + bx + c equals 5 at x = 1. If its derivative is 2x + 1, what are the values of a, b, c respectively?
-
A.
1, 3, 1 -
B.
1, 2, 1 -
C.
2, 1, 1 -
D.
1, 1, 3
Correct Answer: Option D
Explanation
At x = 1, substituting x = 1 in the equation: ax2 + bx + c = 5;
f(1) => a + b + c = 5 …..(1)
Taking the first derivative of f(x) in the original equation gives dy/dx = 2ax + b = 2x + 1 (given)….(2)
From (2),=> b = 1, and 2ax = 2x, => a = 1.
substituting into (1) 1 + 1 + c = 5, => c = 5 – 2 = 3
Thus a = 1, b = 1 and c = 3