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$f(x)$ and $g(x)$ are two differentiable function on [0,2] such that $f''(x)-g''(x)=0$. $f'(1)=2g'(1)=4f(2)=3g(2)=9$ then $f(x)-g(x)$ at $x=\large\frac{3}{2}$ is


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Integrating $f'(x)-g'(x)=c$
$\Rightarrow 4-2=c$
Integrating $f(x)-g(x)=2x+c_1$
$\Rightarrow f(2)-g(2)=4+c_1$
$\Rightarrow 9-3=4+c_1$
At $x=\large\frac{3}{2}$
Hence (d) is the correct answer.
answered Dec 31, 2013 by sreemathi.v

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