JEE Advanced 2015 Paper 2 Mathematics Q14

Mathematics

Problem

Let

f,g:[-1,2]\to\mathbb R

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:

\begin{array}{c|ccc}&x=-1&x=0&x=2\\\hline f(x)&3&6&0\\g(x)&0&1&-1\end{array}

In each of the intervals

(-1,0)

and

(0,2)

the function

(f-3g)''

never vanishes. Then the correct statement(s) is(are)