What is the equation of the normal line of f(x)=(x−1)e−x3−x at x=1?

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Explanation:I&#039;ll first explain my reasoning for what I&#039;m about to do:Find the derivative of the functionFind the gradient of the tangent at x=1Find the gradient of the normal line at x=1Find the y-coordinate at x=1Find the equation of the normal line with the above informationFirstly f′(x)=e−x3−x+(x−1)(−3x2−1)e−x3−x by the product rule.Therefore the gradient at x=1 is given by:f′(1)=e−2+0Therefore the gradient of the normal line at x=1 is:−e2The y-coordinate of the function at x=1 is given by:f(1)=0Finally,In general a straight line is given by:y−y1=m(x−x1)By substituting what we know:y−0=−e2(x−1)Finally:y=−e2x+e2

What is the equation of the normal line

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