Let f(x) and g(x) be twice differentiable fun | vedclass

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(B) Given $f''(x) = g''(x)$. Integrating both sides with respect to $x$,we get $f'(x) = g'(x) + C_1$.From the given conditions,$f'(1) = 4$ and $2g'(1)

Vedclass · Accepted Answer

$40$

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(B) Given $f''(x) = g''(x)$. Integrating both sides with respect to $x$,we get $f'(x) = g'(x) + C_1$.From the given conditions,$f'(1) = 4$ and $2g'(1) = 4 \implies g'(1) = 2$.Substituting these into the derivative equation: $4 = 2 + C_1 \implies C_1 = 2$.Thus,$f'(x) - g'(x) = 2$. Integrating again,we get $f(x) - g(x) = 2x + C_2$.Given $g(2) = 9$ and $3f(2) = 9 \implies f(2) = 3$.Substituting $x = 2$ into the equation $f(x) - g(x) = 2x + C_2$: $3 - 9 = 2(2) + C_2 \implies -6 = 4 + C_2 \implies C_2 = -10$.Therefore,$f(x) - g(x) = 2x - 10$.For $x = 25$,$f(25) - g(25) = 2(25) - 10 = 50 - 10 = 40$.

Let $f(x)$ and $g(x)$ be twice differentiable functions satisfying $f''(x) = g''(x)$ for all $x \in R$,$f'(1) = 2g'(1) = 4$ and $g(2) = 3f(2) = 9$. Then $f(25) - g(25)$ is equal to:

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