What is the equation of the normal line of f(x)=1x2−2x+1 at x=2?

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uvredio0of6 · Accepted Answer

Let&#039;s start by simplifying the function.f(x)=1(x−1)(x−1)f(x)=1x−1Now, let&#039;s start by finding the corresponding y-coordinate to x=2.f(2)=12−1=11=1Next, let&#039;s differentiate the function.f(x)=1x−1By the quotient rule:f′(x)=0×(x−1)−1(1)(x−1)2f′(x)=−1(x−1)2The slope of the tangent (the line that touches the graph at the point x=a) at the point x=2 isf′(2)=−1(2−1)2=−11=−1The normal line is perpendicular to the tangent. So, the slope of the normal line is−1−1=1We now know the normal line&#039;s point of contact on the function (2,1) and the slope of the normal line. We can finally use point-slope form to determine the equation of the normal line.y−y1=m(x−x1)y-1=1(x-2)y-1=x-2y=x-1Hence, the equation of the normal line is y=x-1.

What is the equation of the normal line

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