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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

  1. 2  
  2. 3  
  3. 4  
  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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