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Let f,g : [-1,2] to be continuous funct...

Let `f,g : [-1,2] to` be continuous functions which are twice differentiable on the interval (-1,2). Let the values of f and g at the points and 2 be as given in the following table:

In each of the intervals (-1,0) and (0, 2) the function (f-3g) never vanishes. Then the correct statements(s) is(are) :

A

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

Text Solution

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The correct Answer is:
B, C
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