Question

find the slope of the graph of the function f(x) = √(2x) at (18,6). then find an equation of the line tangent to the graph at that point.
the slope of the graph of the function f(x) = √(2x) at (18,6) is 1/6. (type an integer or a simplified fraction.)
the equation of the line tangent to the graph of f(x) = √(2x) at (18,6) is y = □.

Explanation:

Step1: Recall point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope.
We know that $x_1 = 18$, $y_1=6$ and $m=\frac{1}{6}$.

Step2: Substitute values

Substitute $x_1 = 18$, $y_1 = 6$ and $m=\frac{1}{6}$ into the point - slope form:
$y-6=\frac{1}{6}(x - 18)$

Step3: Simplify the equation

First, distribute $\frac{1}{6}$ on the right - hand side: $y-6=\frac{1}{6}x-3$.
Then, add 6 to both sides of the equation: $y=\frac{1}{6}x + 3$.

Answer:

$y=\frac{1}{6}x + 3$