Question

Write an equation for the tangent line to f(x) = -4x + 3/x at x = -1

How do i solve this?

Answer 1

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.

Answer 2

thank you.

Answer 3

Which would be the correct answer:

A) -7x + y = -6
B) -6x + 2y = -5
C) 7x + y = -6
D) 6x + 2y = -5

Answer 4

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

Answer 5

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

Answer 6

Sure thing

Answer 7

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

Answer 8

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