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The function $4-x^{2}-2y^{2}$

Set $y = 1$

Then <1,1,1>

And its derivative at $y = 1$ is

$$f'(x,1) = -2x$$

The following plot the curve at $y = 1$ intersecting the surface, and the derivative at that point.

My question is, how do I work out the formula to plot a Manipulate plot that allows me to move the tangent (derivative) along the curve in real time? I just can't seem to work out the solution. 

Manipulate[
  ParametricPlot3D[{{t, 1, 2 - t^2}, {1 + t, 1, 1 - 2 t}, {t, -3, 3}, 
    AxesLabel -> {"x", "y", "z"}], 
  {k, -4, 5}]

enter image description here

Michael E2
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    There are already many questions relating to tangents. http://mathematica.stackexchange.com/search?q=tangent Have you made an effort to skim these? – Mr.Wizard Jan 19 '17 at 22:05
  • The first few lines are incomplete sentences, and $f'(x,1)$ is improper notation, however you define $f$, I think. – Michael E2 Jan 19 '17 at 22:42

0 Answers0