JEE Mains · Maths · STD 12 - 1. relation and function
Let \(c, k \in R\). If \(f(x)=(c+1) x^{2}+\left(1-c^{2}\right) x+2 k\) and \(f(x+y)=f(x)+f(y)-x y\), for all \(x, y \in R\), then the value of \(|2( f (1)+ f (2)+ f (3)+\ldots \ldots+ f (20)) \mid\) is equal to
- A \(3365\)
- B \(3375\)
- C \(3385\)
- D \(3395\)
Answer & Solution
Correct Answer
(D) \(3395\)
Step-by-step Solution
Detailed explanation
\(f(x)=(c+1) x^{2}+\left(1-c^{2}\right) x+2 k\) \(\dots(1)\) \(f(x+y)=f(x)+f(y)-x y \quad \forall x y \in R\) \(\lim \limits_{y \rightarrow 0} \frac{f(x+y)-f(x)}{y}=\lim \limits_{y \rightarrow 0} \frac{f(y)-x y}{y}\Rightarrow f^{\prime}(x)=f^{\prime}(0)-x\)…
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