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Let f,g:[-1,2]vecR be continuous functio...

Let `f,g:[-1,2]vecR` be continuous functions which are twice differentiable on the interval `(-1,2)dot` Let the values of `fa n dg` at the points `-1,0a n d2` be as given in the following table: , `x=-1` , `x=0` , `x=2` `f(x)` , 3, 6, 0 `g(x)` , 0, 1, `-1` In each of the intervals `(-1,0)a n d(0,2)` the function `(f-3g)' '` never vanishes. Then the correct statement(s) is (are) `f^(prime)(x)-3g^(prime)(x)=0` has exactly three solutions in `(-1,0)uu(0,2)dot` `f^(prime)(x)-3g^(prime)(x)=0` has exactly one solutions in `(-1,0)dot` `f^(prime)(x)-3g^(prime)(x)=0` has exactly one solutions in `(-1,2)dot` `f^(prime)(x)-3g^(prime)(x)=0` has exactly two solutions in `(-1,0)` and exactly two solutions in `(0,2)dot`

A

`f'(x)-3g'(x)=0` has exactly three solution in `(-1,0) uu (0,2)`

B

`f'(x)-3g'(x)=0` has exactly one solution in (-1,0)

C

`f'(x)-3g'(x)=0` has exactly one solution in (0,2)

D

`f'(x)-3g'(x)=0` has excatly two solutions in (-1,0) and exactly two solution in (0,2)

Text Solution

Verified by Experts

The correct Answer is:
B, C
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