First we needto use implicitdifferentiationto finddy/dxand then substitutethe point(1, 2) into the derivative
to find slope.Thenwe will use the equationof the line (eitherthe slope-interceptform or the point-intercept
form)to find the equationof the tangentline. Usingimplicitdifferentiation,
Now, substitutingpoint(1, 2) into the derivativeto find the slope,
So the slopeof the tangentline is whichis a very smallvalue.(Whatdoesthis tell us aboutthe
orientationof the tangentline?)
Next we needto find the equationof the tangentline. The slope-interceptform is
where andbis they-intercept.To find it, simplysubstitutepoint(1, 2) into the line equation
and solvefor b to find they-intercept.
Thusthe equationof the tangentline is
Remark:we couldhaveusedthe point-slopeform and obtainedthe sameequation.
Example3: