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Maths-

General

Easy

Question

The tangent to the curve $y equals x to the power of 3 end exponent minus 6 x to the power of 2 end exponent plus 9 x plus 4 comma blank 0 less or equal than x less or equal than 5$ has maximum slope at $x$ which is equal to

2
3
4
None of these

The correct answer is: None of these

$because blank y equals x to the power of 3 end exponent minus 6 x to the power of 2 end exponent plus 9 x plus 4$
Now, $fraction numerator d y over denominator d x end fraction equals 3 x to the power of 2 end exponent minus 12 x plus 9$

Let $u equals fraction numerator d y over denominator d x end fraction equals 3 x to the power of 2 end exponent minus 12 x plus 9$

Now, $fraction numerator d u over denominator d x end fraction equals 6 x minus 12$

Put $fraction numerator d u over denominator d x end fraction equals 0$ for maximum or minimum

$therefore blank 6 x minus 12 equals 0$

$rightwards double arrow blank x equals 2$

Now, at $x equals 0 comma blank u equals 9$

at $x equals 2 comma blank u equals negative 3$

and at $x equals 5 comma blank u equals 24$

Thus, the maximum of $u open parentheses x close parentheses comma blank 0 less or equal than x less or equal than 5$ is $u left parenthesis 5 right parenthesis$

Hence, $x equals 5$

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