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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\[
y=
\]

Answer

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Answer

\boxed{y = -105x + 630}

Steps

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

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}