Question

If the function $f\left(x\right)$ defined by $f\left(x\right)=\frac{x^{100}}{100}+\frac{x^{99}}{99}+.....+\frac{x^2}{2}+x+1$, then $f^{\prime }\left(0\right)=$

• A. $100f^{\prime }\left(0\right)$
• B. $1$
• C. $100$
• D. None of these

Answer 1

Answer: (B)

$1$

$f^{\prime }\left(x\right)=x^{99}+x^{98}+...........+x+1$

$f^{\prime }\left(0\right)=0+0+0+.......+0+1$

$f^{\prime }\left(0\right)=1$