+0

# Help

-1
105
2
+3

f(x) = (x-9)/(5x+4)    Find an equation for the tangent line of f at x=8

Sep 26, 2022

#1
+1315
+1

The tangent of f(x) = (x-9)/(5x + 4) would be the asymptote which is x = -1...

Sep 26, 2022
#2
+118471
+1

f(x) = (x-9)/(5x+4)    Find an equation for the tangent line of f at x=8

$$f(8)= \frac{-1}{44}$$

$$f(x) = \frac{(x-9)}{(5x+4)}\\ f'(x)=\frac{(5x+4)(1)-5(x-9)}{(5x+4)^2} \\ f'(x)=\frac{5x+4-5x+45}{(5x+4)^2} \\ f'(x)=\frac{49}{(5x+4)^2} \\ f'(8)=\frac{49}{(44)^2} \\ f'(x)=\frac{49}{1936}$$

Equ of tangent

$$\frac{49}{1936}=\frac{y+\frac{1}{44}}{x-8}\\ 49(x-8)=1936(y+\frac{1}{44})\\ 49x-392=1936y+44\\ 49x-1936y=436$$

I suggest you check this carefully

Sep 28, 2022