QuestionFind an equation of a tangent line to the graph of a $y=f(x)$ at the given point. $$y=x \ln (x-5) \text { at }(6,0)$$ equation: $\square$

Studdy Solution
Use the point-slope form of a line, which is $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is the point $(6, 0)$.
Substitute the values: $$y - 0 = 6(x - 6)$$
Simplify: $$y = 6x - 36$$
The equation of the tangent line is:
$$\boxed{y = 6x - 36}$$