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Maths-
General
Easy

Question

The point(s) on the curve y to the power of 3 end exponent plus 3 x to the power of 2 end exponent equals 12 y where the tangent is vertical is (are)

  1. left parenthesis plus-or-minus 4 divided by square root of 3 right parenthesis    
  2. left parenthesis plus-or-minus square root of 11 divided by 3 end root comma 1 right parenthesis    
  3. left parenthesis 00 right parenthesis    
  4. left parenthesis plus-or-minus 4 divided by square root of 3 comma 2 right parenthesis    

The correct answer is: left parenthesis plus-or-minus 4 divided by square root of 3 comma 2 right parenthesis

    Differentiating the given curve w.r.t x, we get
    3 y to the power of 2 end exponent fraction numerator d y over denominator d x end fraction plus 6 x equals 12 fraction numerator d y over denominator d x end fraction equals fraction numerator d y over denominator d x end fraction equals negative fraction numerator 2 x over denominator y to the power of 2 end exponent minus 4 end fraction
    At point where the tangent(s) is (are) vertical, fraction numerator d y over denominator d x end fraction is not defined, i.e at those points,
    y to the power of 2 end exponent minus 4 equals 0 equals y equals plus-or-minus 2
    when y equals 28 plus 3 x to the power of 2 end exponent equals 12 left parenthesis 2 right parenthesis equals 3 x to the power of 2 end exponent equals 16 equals x equals plus-or-minus fraction numerator 4 over denominator square root of 3 end fraction
    when y equals negative 2 comma negative 8 plus 3 x to the power of 2 end exponent equals negative 24 equals 3 x to the power of 2 end exponent equals negative 16 This is not possible.
    Thus, the required points are left parenthesis plus-or-minus 4 divided by square root of 3 comma 2 right parenthesis

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