# Graphing the tangent to a curve in real time with Manipulate [duplicate]

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}]


## marked as duplicate by m_goldberg, Michael E2, chuy, Mr.Wizard♦ plotting StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Jan 19 '17 at 23:16

• 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