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Maths-

General

Easy

Question

The value of $x$ for which the polynomial $2 x to the power of 3 end exponent minus 9 x to the power of 2 end exponent plus 12 x plus 4$ is a decreasing function of $x$ , is

$- 1 < x < 1$
$0 < x < 2$
$x > 3$
$1 < x < 2$

The correct answer is: $1 less than x less than 2$

Since, $f open parentheses x close parentheses equals 2 x to the power of 3 end exponent minus 9 x to the power of 2 end exponent equals 12 x plus 4$
$rightwards double arrow f to the power of ´ end exponent open parentheses x close parentheses equals 6 x to the power of 2 end exponent minus 18 x plus 12$

For function to be decreasing $f to the power of ´ end exponent left parenthesis x right parenthesis less than 0$

$rightwards double arrow 6 left parenthesis x to the power of 2 end exponent minus 3 x plus 2 right parenthesis less than 0$

$rightwards double arrow open parentheses x minus 2 close parentheses left parenthesis x minus 1 right parenthesis less than 0$

$rightwards double arrow 1 less than x less than 2$

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