Let $f, g:[-1,2] \rightarrow R$ be continuous function which are twice differentiable on the interval $(-1,2)$. Let the values of $f$ and $g$ at the points $-1,0$ and 2 be as given in the following table :
In each of the intervals $(-1,0)$ and $(0,2)$ the function $(f-3 g)$ " never vanishes. Then the correct statement(s) is (are):
Select ALL correct options:
A
(A) $f^{\prime}(x)-3 g^{\prime}(x)=0$ has exactly three solutions in $(-1,0) \cup(0,2)$
B
$f^{\prime}(x)-3 g^{\prime}(x)=0$ has exactly one solution in $(-1,0)$
C
$f^{\prime}(x)-3 g^{\prime}(x)=0$ has exactly one solution in $(0,2)$
D
$f^{\prime}(x)-3 g^{\prime}(x)=0$ has exactly two solutions in $(-1,0)$ and exactly two solutions in $(0,2)$
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In each of the intervals $(-1,0)$ and $(0,2)$ the function $(f-3 g)$ " never vanishes. Then the correct statement(s) is (are):
