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

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riasc31lj · Accepted Answer

Explanation:By definition, the normal line must have a slope that is the opposite reciprocal of the slope of the tangent line at x=1.Thus, to determine the slope of the normal line, we must first calculate the slope of the tangent line at x=1, which is just the derivative of f at x=1 or f&#039;(1).Step 1 Calculate dydxddx[(x−1)2x2+2]=2(x2+2)(x−1)−(x−1)2(2x)(x2+2)2Step 2: Find f&#039;(1)f′(1)=2(3)(0)−(0)2(2)(12+2)3f&#039;(1)=0Step 3: Determine the equation of the normal lineKnowing that f&#039;(1)=0 tells us that there is the graph of f has a horizontal tangent line at x=1. Thus, the normal line must have a slope of ∞ , which is undefined.Because vertical lines are the only type of line with undefined slopes, f must have a vertical tangent line at x=1.The equation for the vertical tangent line is x=1.

What is the equation of the line normal

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