CUET PG 2023 — Mathematics PYQ

1. Find the difference in $f(x)$:

   $$f(1)-f(0)=6-2=4$$

2. Find the difference in $g(x)$:

   $$g(1)-g(0)=2-0=2$$

3. Substitute these into the CMVT formula:

   $$\frac{f^{\prime }(c)}{g^{\prime }(c)}=\frac{4}{2}$$
   $$\frac{f^{\prime }(c)}{g^{\prime }(c)}=2$$

4. Rearrange the equation:

   $$f^{\prime }(c)=2g^{\prime }(c)$$

Conclusion:

For some $c\in (0,1)$, the relationship is: