What is the equation of the line normal to f(x)=(4−2x)2 at x=-3?

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oanhtih6 · Accepted Answer

Explanation:First, find the point the normal line will intercept.f(−3)=(4+6)2=100The normal line will pass through the point (-3, 100).To find the slope of the normal line, we must first know the slope of the tangent line. The slope of the tangent line can be found through calculating f&#039;(-3).First, find f&#039;(x). Through the chain rule,f&#039;(x)=2(4-2x)*(-2)=-4(4-2x)The slope of the tangent line isf&#039;(-3)=-4(4+6)=-40However, the normal line is perpendicular to the tangent line. Perpendicular lines have opposite reciprocal slopes. Thus, the slope of the normal line is the opposite reciprocal of -40 which is 140.Relate the point the normal line intercepts, (-3, 100), and the slope of the line, 140, in an equation in point-slope form:y−100=140(x+3)

What is the equation of the line normal

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