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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!

Would Anyone Care To Explain How To Get Through This Problem In The Photo Im At A Complete Dead End Any Help Would Be Appreciated class=

Sagot :

Trancescient

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]

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