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Maths-

General

Easy

Question

The maximum slope of the curve $y equals negative x to the power of 3 end exponent plus 3 x to the power of 2 end exponent plus 2 x minus 27$ is

5
$- 5$
1/5
None of these

The correct answer is: 5

Given, $y equals negative x to the power of 3 end exponent plus 3 x to the power of 2 end exponent plus 2 x minus 27$
$rightwards double arrow blank fraction numerator d y over denominator d x end fraction equals negative 3 x to the power of 2 end exponent plus 6 x plus 2$

Let slope $z equals fraction numerator d y over denominator d x end fraction equals negative 3 x to the power of 2 end exponent plus 6 x plus 2$

Then, $fraction numerator d z over denominator d x end fraction equals negative 6 x plus 6$

For maximum or minimum put $fraction numerator d z over denominator d x end fraction equals 0 blank$

$rightwards double arrow blank minus 6 x plus 6 equals 0$

$rightwards double arrow blank x equals 1$

Now, $fraction numerator d to the power of 2 end exponent z over denominator d x to the power of 2 end exponent end fraction equals negative 6 less than 0$ , maxima

The maximum value of $z$ at $x equals 1$ , is given by

$z equals negative 3 plus 6 plus 2 equals 5$

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