Question

Would anyone care to explain how to get through this problem in the photo? I'm at a complete dead end! Any help would be appreciated!

Answer 1

Step-by-step explanation:

The slope of the equation tangent to y = f(x) at x = 4 is equal to f'(4). Therefore,

$m = f'(4) = \dfrac{1}{(4)^2 - 9} = \dfrac{1}{7}$

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

$y = mx + b \Rightarrow -1 = \dfrac{1}{7}(4) + b$ or

$b = -\dfrac{11}{7}$

so our equation is

$y = \dfrac{1}{7}x -\dfrac{11}{7}$

or in standard form,

$x - 7y = 11$