Q114 / 160 · WBJEE 2012 · Mathematics

If $f(x)$ and $g(x)$ are twice differentiable. functions on (0,3) satisfying $f^{\prime \prime}(x)=g^{\prime \prime}(x), f^{\prime}(1)=4, g^{\prime}(1)=6, \quad f(2)=3$ $g(2)=9,$ then $f(1)-g(1)$ is

  • A
    4
  • Correct answer
    B
    -4
  • C
    0
  • D
    -2

Solution

According to question, $f^{\prime \prime}(x)=g^{\prime \prime}(x)$ Integrating w.r.t. $x$, we get $\begin{array}{ll} & f^{\prime}(x)=g^{\prime}(x)+c_{1} \\ \text { Put } & x=1 \Rightarrow f^{\prime}(1)=g^{\prime}(1)+C_{1} \\ \Rightarrow & 4=6+C_{1} \\ \therefore & C_{1}=-2 \\ \therefore \quad & f^{\prime}(x)=g^{\prime}(x)-2\end{array}$ Again, integrating w.r.t. $x$, we get $f(x)=g(x)-2 x+C_{2}$ $\Rightarrow \quad 3=9-4+C_{2} \Rightarrow C_{2}=-2$ $\therefore \quad f(x)=g(x)-2 x-2$ Put $x=1,$ we get $f(1)-g(1)=-2(1)-2=-4$

Hence, the correct answer is option: 'B'.

Relevant Questions