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Question

The slope of the tangent to the curve x equals 3 t to the power of 2 end exponent plus 1 comma blank y equals t to the power of 3 end exponent minus 1 at x equals 1 is

  1. fraction numerator 1 over denominator 2 end fraction  
  2. 0  
  3. -2  
  4. infinity  

The correct answer is: 0


    Given, x equals 3 t to the power of 2 end exponent plus 1 and y equals t to the power of 3 end exponent minus 1
    therefore blank fraction numerator d x over denominator d t end fraction equals 6 t and fraction numerator d y over denominator d t end fraction equals 3 t to the power of 2 end exponent

    therefore blank fraction numerator d y over denominator d x end fraction equals fraction numerator d y over denominator d t end fraction cross times fraction numerator d t over denominator d x end fraction equals fraction numerator t over denominator 2 end fraction

    Since, x equals 1 blank rightwards double arrow blank 1 minus 3 t to the power of 2 end exponent plus 1

    rightwards double arrow blank t equals 0

    therefore blank fraction numerator d y over denominator d x end fraction equals 0

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