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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 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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