Calculus Question

Question

Determine the slope of the normal line to the curve y = x+1/x at the point (2,5/2). Round to the nearest hundredth. 

Answer 1

First, find the slope of the curve at (2,5/2).  Call it m₁.  Then the slope of the normal is

 

m₂ = -1/m₁

 

m₁ = y'(2)

 

y'(x) = 1 - 1/x²

 

y'(2) = 1 - 1/2² = 1 - 1/4 = 3/4

 

m₁ = 3/4

 

m₂ = -1/m₁ = -1/(3/4) = -4/3