$\text { Find an equation of the line that is tangent to the graph of } f \text { and parallel to the given }$ line.
$f ( x ) = 3 x ^ { 3 } , 9 x - y + 9 = 0$
A) $y = - 9 x + 6$
B) $y = - 3 x + 6$
C) $y = 9 x - 3$ and $y = 9 x + 3$
D) $y = - 9 x - 6$
E) $y = 9 x - 6$ and $y = 9 x + 6$

Question

Quizplus · Accepted Answer

The given line has a slope of 9. The derivative of $f(x) = 3x^3$ is $f'(x) = 9x^2$. Setting $9x^2 = 9$, we find $x = \pm 1$. The tangent lines at these points are $y = 9x - 6$ and $y = 9x + 6$.

Find an equation of the line that is tangent to the graph of f and parallel to the given \text { Find an equation of the line that is tangent to the graph of } f \text { and parallel to the given } Find an equation of the line that is tangent to the graph of f and parallel to the given

$\text { Find an equation of the line that is tangent to the graph of } f \text { and parallel to the given }$