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Application of Derivatives question

2010 · Shift 0 · Q39

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PYQ Library
JEE Main
Mathematics
Application of Derivatives
2010 · Shift 0 · Q39

Application of Derivatives question

2010 · Shift 0 · Q39

JEE MainMathematicsApplication of DerivativesMCQ+4 / −1

Let

f:R \to R

be a continuous function defined by

f\left( x \right) = {1 \over {{e^x} + 2{e^{ - x}}}}

Statement - 1 :

f\left( c \right) = {1 \over 3},

for some

c \in R

. Statement - 2 :

0 \lt f\left( x \right) \le {1 \over {2\sqrt 2 }},

for all

x \in R

A
Statement - 1 is true, Statement -2 is true; Statement - 2 is not a correct explanation for Statement - 1.
B
Statement - 1 is true, Statement - 2 is false.
C
Statement - 1 is false, Statement - 2 is true.
D
Statement - 1 is true, Statement -2 is true; Statement -2 is a correct explanation for Statement - 1.

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