# Include the Tangent Line with the point slider?

GROUPS:
 Consider the following code: f[x_] := E^x; y[a_, 1/2 _] := f[a] + f'[a]*(x - 1/2); Manipulate[ Show[Plot[ {y[x, 1/2], f[x]}, {x, -2, 4}, {1/2, -2, 4}, PlotStyle -> {Thickness[0.003], Blue}, PlotRange -> {0, 60}], Graphics[{Green, PointSize[0.02], Point[{a, E^a}]}]], {a, -2, 4}] This is what I have so far not sure if I'm heading towards the right direction
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 What, exactly, do you want to illustrate? Just a single tangent line to the curve with a point moving along the curve? (or that but with the point moving along the tangent?) Or do you want a moving tangent line as you move points along the curve?Whichever you want, there are some problems with your code. Before using Manipulate, it's a good idea to try the graphics you want in a static mode, with a fixed value for the control variable(s). your code y[a_, 1/2 _] := f[a] + f'[a]*(x - 1/2)  makes no sense to me: on the left-hand side you seem to have two arguments, the first being a; but what is the second argument? you have 1/2 _, with a space between the fraction and the pattern symbol _; what is that supposed to mean? Moreover, you have an x on the right-hand side but no x as an argument. your Plot code Plot[ {y[x, 1/2], f[x]}, {x, -2, 4}, {1/2, -2, 4} (* options *)]  makes no sense: you seem to want to plot two functions of variable x, namely, y[x, 1/2] and f[x], but then after the domain list {x, -2, 4} (which is fine) you have the mysterious list {1/2, -2, 4}.Once you straighten all that out, you can try to put it inside the Manipulate.I also suggest that you not directly use f'[a] but rather compute ahead of time, once and for all, the derivative functions, say: fp[x_] = f'[x] And then use that in the right-hand side f[a] + fp[a] (x - 1/2) (or whatever it is that you really are trying to get there).Note also that there is no earthly reason to include the explicit * symbol for multiplication in f[a] + f'[a] * (x - 1/2) or similar symbolic expression; explicit multiplication signs are needed in Mathematica only between actual numbers.
 I might use Series to compute the tangent line: f[x_] := E^x; Manipulate[ With[{tl = Normal@Series[f[x], {x, a, 1}]}, Show[ Plot[{tl, f[x]}, {x, -2, 4}, PlotStyle -> {Thickness[0.003], Blue}, PlotRange -> {0, 60}], Graphics[{Green, PointSize[0.02], Point[{a, E^a}]}] ] ], {a, -2, 4}]