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

For the curve...

Question

For the curve $y = 4 x - 2 x^{2}$ , find the equation of tangent passes through the origin.

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Solution

The equation is $y = 4 x - 2 x^{2}$
The slope of tangent is given as $\frac{d y}{d x} = \frac{d}{d x} 4 x - 2 x^{2} \frac{d y}{d x} = 4 - 4 x {\frac{d y}{d x} ∣ ∣ ∣}_{(0.0)} = 4$
The equation of tangent passing through origin is $y - 0 = 4 (x - 0) y = 4 x$

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