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

Explanation:

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

`m = f'(4) = (1)/((4)^2 - 9) = (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 = (1)/(7)(4) + b` or

`b = -(11)/(7)`

so our equation is

`y = (1)/(7)x -(11)/(7)`

or in standard form,

`x - 7y = 11`