• Support PF! Buy your school textbooks, materials and every day products Here!

Weird calculus problem

Which of the following is an equation of a curve that intersects at right angles every curve of the family y = 1/x + k where k takes all real values?
a)y= -x b)y= -x^2 c)y= -x^3/3 d)y=x^3/3 e)y=ln x
 

NateTG

Science Advisor
Homework Helper
2,449
5
Are you sure that you don't mean
[tex]y=\frac{1}{x} + k[/tex]

then [tex]\frac{dy}{dx}=\frac{-1}{x^2}[/tex]

any suitable function would have the negative reciprocal slope, so
[tex]\frac{df}{dx}=\frac{x^2}{1}=x^2[/tex]
sp
[tex]f(x)=\frac{x^3}{3}+C[/tex]

and the answer is d.
 

Related Threads for: Weird calculus problem

  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
14
Views
5K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
9K
  • Last Post
Replies
2
Views
969
  • Last Post
Replies
7
Views
4K
  • Last Post
Replies
9
Views
1K
  • Last Post
Replies
5
Views
1K

Recent Insights

Top