What is the equation of the normal line

Eddie Clarke

Eddie Clarke

Answered question


What is the equation of the normal line of f(x)=x2x at x=2?

Answer & Explanation



Beginner2022-04-10Added 10 answers

The normal line will be perpendicular to the tangent line when x=2.
We can determine what point on f(x) the normal line will intersect by finding that
f(2)=2, so the point is (2,2).
If we already have a point on the normal line, all we need to know is its slope. We can find of the tangent line when x=2 by finding f'(2). Since the normal line is perpendicular to the tangent line, its slope will be the opposite reciprocal of the tangent line's.
Finding f'(x) will require use of the chain rule.
f(x)=12(x2x)12d dx [x2x]
Find the slope of the tangent line.
Take the opposite reciprocal to find that the slope of the normal line is 223.
Remember that it passes through the point (2,2).
Write the equation in point-slope form:
In slope-intercept form:

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