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Maths-

General

Easy

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

0
$\frac{1}{2}$
$\infty$
$- 2$

The correct answer is: 0

Given curve is $x equals 3 t to the power of 2 end exponent plus 1 comma blank y equals t to the power of 3 end exponent minus 1$
For $x equals 1 comma blank 3 t to the power of 2 end exponent plus 1 equals 1 blank rightwards double arrow blank t equals 0$

$therefore blank fraction numerator d x over denominator d t end fraction equals 6 t comma blank fraction numerator d y over denominator d x end fraction equals 3 t to the power of 2 end exponent$

Now, $fraction numerator d y over denominator d x end fraction equals open parentheses fraction numerator fraction numerator d y over denominator d t end fraction over denominator fraction numerator d x over denominator d t end fraction end fraction close parentheses equals fraction numerator 3 t to the power of 2 end exponent over denominator 6 t end fraction equals fraction numerator t over denominator 2 end fraction$

$therefore blank open parentheses fraction numerator d y over denominator d x end fraction close parentheses subscript left parenthesis t equals 0 right parenthesis end subscript equals fraction numerator 0 over denominator 2 end fraction equals 0$

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