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Let g(x)=int0^x(3t^(2)+2t+9)dt and f(x) ...

Let `g(x)=int_0^x(3t^(2)+2t+9)dt and f(x) ` be a decreasing function `forallxge0` such that `AB=f(x)hat(i)+g(x)hat(j) and AC=g(x)hat(i)+f(x)hat(j)` are the two smallest sides of a triangle ABC whose circumcentre lies outside the triangle `forall cgto.` Q. Which of the following is true (for `xgeo)`

A

`f(x) gt 0, g(x) lt 0`

B

`f(x) lt 0, g(x) lt 0`

C

`f(x) gt 0, g(x) gt 0`

D

`f(x) lt 0, g(x) gt 0`

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The correct Answer is:
D
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