MHT CET · Maths · Differentiation
The valuc of \(f(4)-f(3)\) is
- A \(\Delta f(2)+\Delta^{2} f(1)+\Delta^{3} f(1)\)
- B \(\Delta f(3)+\Delta^{2} f(2)+\Delta^{3} f(1)\)
- C \(\Delta f(2)+\Delta^{2} f(1)+\Delta^{3} f(0)\)
- D None of the above
Answer & Solution
Correct Answer
(A) \(\Delta f(2)+\Delta^{2} f(1)+\Delta^{3} f(1)\)
Step-by-step Solution
Detailed explanation
\(f(4)-f(3)=\Delta f(3)\)
\(=\Delta[f(2)+\Delta f(2)]\)
\([\because \Delta f(2)=f(3)-f(2)]\)
\(=\Delta f(2)+\Delta^{2} f(2)\)
\(=\Delta f(2)+\Delta^{2}[f(1)+\Delta f(1)]\)
\(=\Delta f(2)+\Delta^{2} f(1)+\Delta^{3} f(1)\)
\(=\Delta[f(2)+\Delta f(2)]\)
\([\because \Delta f(2)=f(3)-f(2)]\)
\(=\Delta f(2)+\Delta^{2} f(2)\)
\(=\Delta f(2)+\Delta^{2}[f(1)+\Delta f(1)]\)
\(=\Delta f(2)+\Delta^{2} f(1)+\Delta^{3} f(1)\)
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