How do you find the equation of the tangent line to the graph of the given function f(x)=x^2-2x+1 ; at (-1,-1)?
First you need to find the derivative of your function:
f(x)=2x-2
Now yoy evaluate the derivative in x=-1;
f(-1)=2.(-1)-2=-4
this is the slope m of the tangent.
y-y_0=m(x-x_0) to find the equation of the tangent,
y+1=-4(x+1)
y+1=-4x-4
y=-4x-5