Application of Derivatives PYQ — JEE Advanced 2015 · Shift 2 · Q33 with Solution

Let

f, g :

\left[ { - 1,2} \right] \to 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:

	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
$f'\left( x \right) - 3g'\left( x \right) = 0$ has exactly three solutions in $\left( { - 1,0} \right) \cup \left( {0,2} \right)$
B
$f'\left( x \right) - 3g'\left( x \right) = 0$ has exactly one solution in $(-1, 0)$
C
$f'\left( x \right) - 3g'\left( x \right) = 0$ has exactly one solution in $(0, 2)$
D
$f'\left( x \right) - 3g'\left( x \right) = 0$ has exactly two solutions in $(-1, 0)$ and exactly two solutions in $(0, 2)$

Application of Derivatives question