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Equation of Tangent at a Point (x,y) in Terms of f'(x)

Equation of t...

Question

Equation of the normal line to $y = log x$ at the point at which the curve crosses $x - a x i s$ is

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Solution

$y = log x$ cuts $x$ axis at $x = 1$
Slope of tangent at $x = 1$ is $y = log x$
$\frac{d y}{d x} = \frac{1}{x}$
Slope $= 1$
Slope of normal at $x = 1$ is $- 1$
Equation of normal point $(0, 1)$ $m = - 1$
$y - 0 = - 1 (x - 1)$
$⟹ y = - x + 1$
$⟹ x + y = 1$

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Equation of Tangent at a Point (x,y) in Terms of f'(x)

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