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Application of Derivatives question

2016 · Shift 2 · Q28

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PYQ Library
JEE Advanced
Mathematics
Application of Derivatives
2016 · Shift 2 · Q28

Application of Derivatives question

2016 · Shift 2 · Q28

JEE AdvancedMathematicsApplication of DerivativesMultiple correct+4 / −2

Let f: R

\to \left( {0,\infty } \right)

and g : R

\to

R be twice differentiable functions such that f'' and g'' are continuous functions on R. Suppose f'

(2)=

g

(2)=0

, f''

(2) e 0

and g'

(2) e 0

. If

\mathop {\lim }\limits_{x \to 2} {{f\left( x \right)g\left( x \right)} \over {f'\left( x \right)g'\left( x \right)}} = 1,

then

A
$f$ has a local minimum at $x=2$
B
$f$ has a local maximum at $x=2$
C
$f''(2)>f(2)$
D
$f(x)-f''(x)=0$ for at least one $x \in R$

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