## ZeroAT 2 years ago Write an equation for the tangent line to f(x) = -4x + 3/x at x = -1 How do i solve this?

1. LolWolf

So, we need to know the slope at this point, this is given by: $\frac{d}{dx}\left(-4x+\frac{3}{x}\right)=-4-\frac{3}{x^2}$Evaluating this at $$x=-1$$: $-4-\frac{3}{x^2}\Bigg|_{x=-1}=-4+3=-1$So the slope of the line is -1 at this point. Now, find a point on the line: $-4(-1)+\frac{3}{-1}=-7=y$Which means: $y+7=-1(x+1)$Et voilá.

2. ZeroAT

thank you.

3. ZeroAT

Which would be the correct answer: A) -7x + y = -6 B) -6x + 2y = -5 C) 7x + y = -6 D) 6x + 2y = -5

4. LolWolf

Wait, I screwed up, it's: $-4-\frac{3}{x^2}\Bigg|_{x=-1}=-4-3=-7$So: $y+7=-7(x+1)$

5. ZeroAT

oh! that explains why i coudnt get the answer. Thanks for the assistance

6. LolWolf

Sure thing

7. ZeroAT

One more question..How would i get the end results in one of those 4 possible results i mentioned? can you show me?

8. LolWolf

Just solve for the same form, it's roughly the same case.