Step-by-step explanation:
The slope of the equation tangent to y = f(x) at x = 4 is equal to f'(4). Therefore,
[tex]m = f'(4) = \dfrac{1}{(4)^2 - 9} = \dfrac{1}{7}[/tex]
We also know that the line passes through the tangent point at (4, -1) so we can write the slope-intercept form of the equation as
[tex]y = mx + b \Rightarrow -1 = \dfrac{1}{7}(4) + b[/tex] or
[tex]b = -\dfrac{11}{7}[/tex]
so our equation is
[tex]y = \dfrac{1}{7}x -\dfrac{11}{7}[/tex]
or in standard form,
[tex]x - 7y = 11[/tex]
