Find the equation of the tangent to the curve $y = 3 x^{2}$ at $(1, 1)$ .

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Solution

Slope of the tangent to the curve at any point $(x, y) = \frac{d y}{d x}$ at $(x, y)$
$\frac{d y}{d x} = \frac{d (3 x^{2})}{d x} = 6 x$
At $(1, 1)$ , the slope of the tangent would be $6$
Hence, the equation of line passing through $(1, 1)$ and having a slope of $6$ is given by
$y - 1 = 6 (x - 1)$
$\Rightarrow 6 x - y = 5$

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