Find the slope of the tangent to the curve $y = x^{3} - x$ at $x = 2$ .

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Solution

$y = x^{3} - x$ at $x = 2$
Diff wrt $x$
$\frac{d y}{d x} = 3 x^{2} - 1$
Slope of tangent $= \frac{d y}{d x} |_{x = 2} = 3 (2^{2}) - 1$
$= 12 - 1$
$∴$ Slope of tangent $= 11$ .

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