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Maths-

General

Easy

Question

A function $f$ is defined by $f open parentheses x close parentheses equals e to the power of x end exponent sin invisible function application x$ in $left square bracket 0 comma blank pi right square bracket$ . Which of the following is not correct?

$f$ is continous in $[0, π]$
$f$ is differentiable in $[0, π]$
$f (0) = f (π)$
Rolle’s theorem is not true in $[0, π]$

The correct answer is: Rolle’s theorem is not true in $left square bracket 0 comma blank pi right square bracket$

Given, $f open parentheses x close parentheses equals e to the power of x end exponent sin invisible function application x comma blank x element of open square brackets 0 comma blank pi close square brackets$
At $x equals 0 comma blank f open parentheses 0 close parentheses equals 0$

And at $x equals pi comma blank f open parentheses pi close parentheses equals 0$

Also, it is continuous and differentiable in the given interval.

Hence, it satisfies the Rolle’s theorem.

Hence, option (d) is the required answer

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