Find the equation of the tangent to the curve $y = - 5 x^{2} + 6 x + 7$ at the point $(1 / 2, 35 / 4)$ .

y = x - \frac{33}{4}

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x = y + \frac{33}{4}

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y = x + \frac{33}{4}

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Solution

The correct option is C $y = x + \frac{33}{4}$
The equation of the given curve is :
$y = - 5 x^{2} + 6 x + 7$
$\frac{d y}{d x} = - 10 x + 6$

$(\frac{d y}{d x})_{1 / 2, 35 / 4} = - \frac{10}{2} + 6 = 1$

The required equation of the tangent is :
$y - \frac{35}{4} = 1 (x - \frac{1}{2})$

$y = x + \frac{33}{4}$

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