How do you find the tangent line to the curve #y=x^3-9x# at the point where #x=1#?
So, the point we are targeting is
To find the slope of the tangent line there, we must differentiate
So, the slope of the tangent line is
Now, we use the point-slope formula to compute the equation, that is,
#(x_0,y_0)#are the original coordinates
Therefore, we get,
A graph shows it: