use implicit differentiation to find an equation of the tangent line to the curve at the given point.?
I got the derivative as..
2x−2x+4
But when I plug in the points I get the equation y=x/2+2 which is wrong. Is my derivative wrong? Or am I making a mistake plugging my numbers in. If you could show me where I’m going wrong it’d be much appreciated.
use implicit differentiation to find an equation of the tangent line to the curve at the given point.?
I’m getting a very different derivative. Here’s how I did it
3=x2+xy+y2
Now we differentiate
0=2x+xdydx+y+2ydydx
Separate terms
−(2x+y)=dydx(x+2y)
so
dydx=−(2x+y)x+2y
Plugging in (1,1), we get dydx=−(2+1)1+2=−33=−1, so the tangent line at (1,1), in point-slope form, is y−1=−(x−1), or y=−x+2
use implicit differentiation to find an equation of the tangent line to the curve at the given point.?
x2+xy+y2=32x+xdydx+y+2ydydx=0dydx=−2x+yx+2y
At (1,1), dydx=−1. So, y−1=−(x−1)=1−x. So, y=2−x is the equation for the tangent line.