Find the equation of the tangent line to the function $f$ at $x = 6$ .
$f (x) = - 9 x^{2} + 3 x - 8$
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$y =$

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Answer

\boxed{y = -105x + 630}

Steps

Step 1 ：Find the derivative of the function: $f^{'} (x) = - 18 x + 3$

Step 2 ：Evaluate the derivative at $x = 6$ : $f^{'} (6) = - 105$

Step 3 ：Find the value of the function at $x = 6$ : $f (6) = - 314$

Step 4 ：Use the point-slope form to find the equation of the tangent line: $y + 314 = - 105 (x - 6)$

Step 5 ：\boxed{y = -105x + 630}