Q9Multiple correct4 Marks1 Dec 2024

Let $f$ be a polynomial of degree $5$, given by $f(x)=a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0$. Let $f'(b)$ denote the derivative of $f$ at $x=b$. Choose the set of correct options.

A

$a_1=f'(0)$.

B

$5a_5+3a_3=\frac{1}{2}\{f'(1)+f'(-1)-2f'(0)\}$.

C

$4a_4+2a_2=\frac{1}{2}\{f'(1)-f'(-1)\}$.

D

$a_1=f'(1)$.