What is the equation of the normal line of #f(x)=x^2 # at #x=5 #?
1 Answer
Dec 4, 2015
Explanation:
The normal line is the line perpendicular to the tangent line. Then, the steps are as follows:

Find the slope
#m_"tangent"# of tangent line
Find the first derivative of the function
Evaluate the first derivative at the desired point 
Find the slope
#m_"norm"# of the normal line
Let#m_"norm" = 1/m_"tangent"# 
Find the line with slope
#m_"norm"# passing through the given point
Using pointslope form:#(yy_1) = m_"norm"(xx_1)#
Let's go through the process.
Substituting, we get the equation of the normal line.