What is the equation of the normal line

Blaze Shepherd

Blaze Shepherd

Answered question

2022-04-09

What is the equation of the normal line of f(x)=xx22 at x=2?

Answer & Explanation

Wernbergbo9d

Wernbergbo9d

Beginner2022-04-10Added 12 answers

Firstly, f(2)=2222=0.
Thus the point (2,0) lies on the graph of f at the point 2.
Now the derivative f'(x)=1-x,
and evaluated at the point 2 we get f'(2)=1-2=-1.
This means that the gradient of the function f at the point when x=-2 is -1.
Now a line normal at this point is perpendicular and will hence have a gradient of 1 since the product of gradients of perpendicular lines must be -1.
Bu t a normal line is still a straight line so has a linear equation of form y=mx+c
If we substitute the point (2, 0) and the gradient 1 into this linear equation we get
0=2+cc=2
Therefore the equation of the required normal line is y=x-2.

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