Q: Let f(x) = -2/x . Find the equation of the tangent line when x = -1.
A: First, let’s take the derivative….
f(x) = -2/x
Re-write this as:
f(x) = -2x-1
Now, take the derivative using the power rule:
f ‘(x) = (-1)-2x-1-1
f ‘(x) = 2x-2
Now, plug in x = -1 to the derivative:
f ‘(-1) = 2(-1)-2
f ‘(-1) = 2
So, the slope of the graph when x = -1 is 2….
To find the equation of the tangent line, I always like to start with:
y = mx + b
Our slope (m) is 2.. we just found that. So,
y = 2x + b
Now we need to solve for “b” and we are done! In order to do this, I need an (x, y) point. Well, I know x = -1… so I need to find the y that goes along with that x… To do this, I go back to the original equation:
f(x) = -2/x
Plug in x = -1:
f(-1) = -2/-1 = 2
Therefore, my (x, y) point is (-1, 2)….
So,
y = 2x + b
Plug in my point:
2 = 2(-1) + b
2 = -2 + b
4 = b
Therefore, the equation of my tangent line when x = 1 is:
y = 2x + 4
dont we subtract 2 from
-2 = 2 + b
-4=b?
it says finally answer y=2x+4
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Yes… The error I had made originally was that I accidentally plugged in x=1 and it should have been x=-1!! It has been fixed!
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got cha! 🙂 thanks
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