Labware - MA35 Multivariable Calculus - Single Variable Calculus



Tangent Lines and Normal Vectors (Page: 1 | 2 )


If a function f(x) is differentiable at x0, then f(x) will have a tangent line at (x0) with the equation l(x) = f(x0) + f '(x0)(x - x0).

The normal vector at x0, (-f '(x0), 1), is perpendicular to the tangent line.



  • 1. Find equations for the tangent line for each of the following sets of conditions, and check using one of the demos:
    • f(x) = x2 at x = 1
    • f(x) = sin(x) at x = π
    • f(x) = |x| at x = 1
  • 2. Why is the tangent line not defined for f(x) = |x| at x = 0?
  • 3. Describe the tangent lines and normal vectors for any linear function.
  • 4. Note that since the normal vector in this demo always has a vertical component of 1, it can never be parallel to the x-axis. Is this a problem? Why or why not?