Finding equation of tangent line at a point

Question

my function is defined as:

f[x_] = x^1.1 - 2.5 x^.5

I need to find the equation of the tangent line to the curve using the point slope form which would be something like:

f'[a][x+a]+f[a]

$a=1$ and $x=1$ in the instance

How would I type this?

Answer 1

Having

f[x_] := x^1.1 - 2.5 x^.5

And also knowing that the formula of the tangent line is

f'[x](x-a) + f[a]

You could just make a Plot with it.

With a=1, as you requested:

Here is the code of it:

With[
 {a = 1},
  Plot[
   {
    f[x],
    f'[a] (x - a) + f[a]
    },
   {x, 0, 10},
   PlotRange -> {-4, 4},
   PlotStyle -> Thick,
   Epilog -> {PointSize[Large], Point[{a, f[a]}]}
   ]
 ]