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Maths-

General

Easy

Question

The values of $a$ in order that $f open parentheses x close parentheses equals square root of 3 sin invisible function application x minus cos invisible function application x minus 2 a x plus b$ decreases for all real values of $x$ , is given by

$a < 1$
$a \geq 1$
$a \leq \sqrt{2}$
$a < \sqrt{2}$

The correct answer is: $a greater or equal than 1$

Given, $f to the power of ´ end exponent open parentheses x close parentheses less than 0 comma blank for all blank x element of R$
$rightwards double arrow blank square root of 3 cos invisible function application x plus sin invisible function application x minus 2 a less than 0 comma blank for all blank x element of R$

$rightwards double arrow blank fraction numerator square root of 3 over denominator 2 end fraction cos invisible function application x plus fraction numerator 1 over denominator 2 end fraction sin invisible function application x less than a comma blank for all blank x element of R$

$rightwards double arrow sin invisible function application open parentheses x plus fraction numerator pi over denominator 3 end fraction close parentheses less than a comma blank for all blank x blank element of R$

$rightwards double arrow blank a greater or equal than 1 blank open square brackets because blank sin invisible function application open parentheses x plus fraction numerator pi over denominator 3 end fraction close parentheses less or equal than 1 close square brackets$

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