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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

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

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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