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Let f,g:[-1,2]rarr RR be continuous func...

Let `f,g:[-1,2]rarr RR` be continuous functions 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 : `x=-1 x=0 x=2 f(x) 3 6 0 g(x) 0 1 -1` In each of the intervals (-1,0) and (0, 2) the function (f – 3g)'' never vanishes. Then the correct statement(s) is(are)

A

f(x) -3g(x)=0 has exactly three solutions 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 exactly two solutions in (-1,0) and exactly two solutions in (0.2)

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The correct Answer is:
B, C
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