Simple Tangent Line Grapher

## Description

Here is a Sage interact that plots a tangent line to a given function. The `xbegin` and `xend` sliders control the endpoints of the graphed curve, and `x0` controls the point at which the tangent is calculated.

## Sage Cell

#### Code

```
pretty_print(html('<h2>Tangent line grapher</h2>'))
@interact
def tangent_line(f = input_box(default=sin(x)), xbegin = slider(0,10,1/10,0), xend = slider(0,10,1/10,10), x0 = slider(0, 1, 1/100, 1/2)):
prange = [xbegin, xend]
x0i = xbegin + x0*(xend-xbegin)
var('x')
df = diff(f)
tanf = f(x=x0i) + df(x=x0i)*(x-x0i)
fplot = plot(f, prange[0], prange[1])
print('Tangent line is y = ' + tanf._repr_())
tanplot = plot(tanf, prange[0], prange[1], rgbcolor = (1,0,0))
fmax = f.find_local_maximum(prange[0], prange[1])[0]
fmin = f.find_local_minimum(prange[0], prange[1])[0]
show(fplot + tanplot, xmin = prange[0], xmax = prange[1], ymax = fmax, ymin = fmin)
```

## Options

none

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Date: 19 Jul 2020 02:56

Submitted by: Zane Corbiere