Question

find y
$y = \frac{3}{x^2 + 9}$
find the slope of the line tangent to the graph of $y = \arctan\left(\frac{x}{3}\
ight)$ at the point $\left(3, \frac{\pi}{4}\
ight)$.
$\frac{1}{6}$
find an equation for the tangent line to the graph of the function $y = \arctan\left(\frac{x}{3}\
ight)$ at the point $\left(3, \frac{\pi}{4}\
ight)$.
$y = \frac{1}{6}(x - 3)$
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Explanation:

Step1: Recall point-slope formula

The point-slope form of a line is $y - y_1 = m(x - x_1)$, where $m$ is the slope, and $(x_1, y_1)$ is the point on the line.

Step2: Identify known values

We know $m = \frac{1}{6}$, $x_1 = 3$, $y_1 = \frac{\pi}{4}$.

Step3: Substitute into point-slope form

$y - \frac{\pi}{4} = \frac{1}{6}(x - 3)$

Step4: Rearrange to solve for y

$y = \frac{1}{6}(x - 3) + \frac{\pi}{4}$

Answer:

$y = \frac{1}{6}(x - 3) + \frac{\pi}{4}$