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If , be twice differentiable function on satisfying = , , and , , then at equals ->
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The answer is -10.
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1 solution
If f''(x) = g''(x), then integration with respect to x gives:
f'(x) = g'(x) + A
and inputting the boundary conditions f'(1) = 2, g'(1) = 4 gives A = -2, or f'(x) = g'(x) - 2.
Now integrating again gives:
f(x) = g(x) - 2x + B
and inputting f(2) = 3 , g(2) = 9 gives:
3 = 9 -2(2) + B => B = -2
or f(x) = g(x) - 2x - 2;
or f(x) - g(x) = -2(x + 1).
Hence at x = 4, (f - g)(4) = f(4) - g(4) = -2(4 + 1) = -10.