Let f: R \to R be a continuous function defined by f(x)=\frac{1}{e^x+2 e^{-x}} Statement - 1: f(c)=\frac{1}{3}, for some c \in R. Statement - 2: 0< f(x) \leq {1}/{2 \sqrt{2}}, for all x \in R [AIEEE 2010]

Correct Answer is : Statement −1 is true, Statement −2 is true; Statement −2 is a correct explanation for Statement - 1.

Statement - 1 is true, Statement -2 is true; Statement - 2 is not a correct explanation for Statement - 1.

Statement -1 is true, Statement -2 is false.

Statement -1 is false, Statement -2 is true.

Statement -1 is true, Statement -2 is true; Statement -2 is a correct explanation for Statement - 1.

Application of Derivatives Part 1

Section: Mathematics

Question : 76 of 100

Marks: +1, -0

Let f:R→R be a continuous function defined by
f(x)=‌

ex+2e−x

Statement - 1: f(c)=‌

, for some c∈R.
Statement - 2:0<f(x)≤‌

2√2

, for all x∈R

[AIEEE 2010]

Statement - 1 is true, Statement −2 is true; Statement - 2 is not a correct explanation for Statement - 1.
Statement −1 is true, Statement −2 is false.
Statement −1 is false, Statement −2 is true.
Statement −1 is true, Statement −2 is true; Statement −2 is a correct explanation for Statement - 1.

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