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Question

If f(x),g(x) be twice differentiable functions on [0,2] satisfyingf"(x)=g"(x),f(1)=2g(1)=4 and f(2)=3g(2)=9, then f(x)g(x) at x=4equals

A
0
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B
10
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C
8
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D
2
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Solution

The correct option is C 10
Given, f′′=g′′
f(1)=2g(1)=4
f(x)=3g(2)=9
f(x)g(x)=h(x)
h(x)=f(x)g(x)
h(1)=2
h′′(x)=f′′(x)g′′(x)=0
h(2)=f(2)g(2)
=93=6
h(2)=6
h(x)=ax2+bx+c
4a+2b+c=6
2a+b=2
a=0b=2
4+c=6
c=2
Therefore, e2x+2=h(x)
h(4)=10

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