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(x0i) + df(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_maximum_on_interval(prange[0], prange[1])[0]
fmin = f.find_minimum_on_interval(prange[0], prange[1])[0]
show(fplot + tanplot, xmin = prange[0], xmax = prange[1], ymax = fmax, ymin = fmin)