f(x)

f'(x)

show derivative

show function

show tangent

maxx = 3
x_{0} = 2.92
x_{1} = 2.35
x_{2} = 1.3
x_{3} = 0
x_{4} = -1.3
x_{5} = -2.35
x_{6} = -2.92
vline_{0}: x = x_{0}
vline_{1}: x = x_{1}
vline_{2}: x = x_{2}
vline_{3}: x = x_{3}
vline_{4}: x = x_{4}
vline_{5}: x = x_{5}
vline_{6}: x = x_{6}
A_{0} = Point(vline_{0})
A_{1} = Point(vline_{1})
A_{2} = Point(vline_{2})
A_{3} = Point(vline_{3})
A_{4} = Point(vline_{4})
A_{5} = Point(vline_{5})
A_{6} = Point(vline_{6})
y_{0}: y(A_{0})
y_{1}: y(A_{1})
y_{2}: y(A_{2})
y_{3}: y(A_{3})
y_{4}: y(A_{4})
y_{5}: y(A_{5})
y_{6}: y(A_{6})
p_{0}(x) = y_{0} * (x - x_{1}) * (x - x_{2}) * (x - x_{3}) * (x - x_{4}) * (x - x_{5}) * (x - x_{6}) / ((x_{0} - x_{1}) * (x_{0} - x_{2}) * (x_{0} - x_{3}) * (x_{0} - x_{4}) * (x_{0} - x_{5}) * (x_{0} - x_{6}))
p_{1}(x) = y_{1} * (x - x_{0}) * (x - x_{2}) * (x - x_{3}) * (x - x_{4}) * (x - x_{5}) * (x - x_{6}) / ((x_{1} - x_{0}) * (x_{1} - x_{2}) * (x_{1} - x_{3}) * (x_{1} - x_{4}) * (x_{1} - x_{5}) * (x_{1} - x_{6}))
p_{2}(x) = y_{2} * (x - x_{0}) * (x - x_{1}) * (x - x_{3}) * (x - x_{4}) * (x - x_{5}) * (x - x_{6}) / ((x_{2} - x_{0}) * (x_{2} - x_{1}) * (x_{2} - x_{3}) * (x_{2} - x_{4}) * (x_{2} - x_{5}) * (x_{2} - x_{6}))
p_{3}(x) = y_{3} * (x - x_{0}) * (x - x_{1}) * (x - x_{2}) * (x - x_{4}) * (x - x_{5}) * (x - x_{6}) / ((x_{3} - x_{0}) * (x_{3} - x_{1}) * (x_{3} - x_{2}) * (x_{3} - x_{4}) * (x_{3} - x_{5}) * (x_{3} - x_{6}))
p_{4}(x) = y_{4} * (x - x_{0}) * (x - x_{1}) * (x - x_{2}) * (x - x_{3}) * (x - x_{5}) * (x - x_{6}) / ((x_{4} - x_{0}) * (x_{4} - x_{1}) * (x_{4} - x_{2}) * (x_{4} - x_{3}) * (x_{4} - x_{5}) * (x_{4} - x_{6}))
p_{5}(x) = y_{5} * (x - x_{0}) * (x - x_{1}) * (x - x_{2}) * (x - x_{3}) * (x - x_{4}) * (x - x_{6}) / ((x_{5} - x_{0}) * (x_{5} - x_{1}) * (x_{5} - x_{2}) * (x_{5} - x_{3}) * (x_{5} - x_{4}) * (x_{5} - x_{6}))
p_{6}(x) = y_{6} * (x - x_{0}) * (x - x_{1}) * (x - x_{2}) * (x - x_{3}) * (x - x_{4}) * (x - x_{5}) / ((x_{6} - x_{0}) * (x_{6} - x_{1}) * (x_{6} - x_{2}) * (x_{6} - x_{3}) * (x_{6} - x_{4}) * (x_{6} - x_{5}))
p(x) = p_{0}(x) + p_{1}(x) + p_{2}(x) + p_{3}(x) + p_{4}(x) + p_{5}(x) + p_{6}(x)
maxy = 8
pdiff_{0}(x) = (y_{0} * ((x - x_{2}) * (x - x_{3}) * (x - x_{4}) * (x - x_{5}) * (x - x_{6}) + (x - x_{1}) * (x - x_{3}) * (x - x_{4}) * (x - x_{5}) * (x - x_{6}) + (x - x_{1}) * (x - x_{2}) * (x - x_{4}) * (x - x_{5}) * (x - x_{6}) + (x - x_{1}) * (x - x_{2}) * (x - x_{3}) * (x - x_{5}) * (x - x_{6}) + (x - x_{1}) * (x - x_{2}) * (x - x_{3}) * (x - x_{4}) * (x - x_{6}) + (x - x_{1}) * (x - x_{2}) * (x - x_{3}) * (x - x_{4}) * (x - x_{5}))) / ((x_{0} - x_{1}) * (x_{0} - x_{2}) * (x_{0} - x_{3}) * (x_{0} - x_{4}) * (x_{0} - x_{5}) * (x_{0} - x_{6}))
pdiff_{1}(x) = (y_{1} * ((x - x_{2}) * (x - x_{3}) * (x - x_{4}) * (x - x_{5}) * (x - x_{6}) + (x - x_{0}) * (x - x_{3}) * (x - x_{4}) * (x - x_{5}) * (x - x_{6}) + (x - x_{0}) * (x - x_{2}) * (x - x_{4}) * (x - x_{5}) * (x - x_{6}) + (x - x_{0}) * (x - x_{2}) * (x - x_{3}) * (x - x_{5}) * (x - x_{6}) + (x - x_{0}) * (x - x_{2}) * (x - x_{3}) * (x - x_{4}) * (x - x_{6}) + (x - x_{0}) * (x - x_{2}) * (x - x_{3}) * (x - x_{4}) * (x - x_{5}))) / ((x_{1} - x_{0}) * (x_{1} - x_{2}) * (x_{1} - x_{3}) * (x_{1} - x_{4}) * (x_{1} - x_{5}) * (x_{1} - x_{6}))
pdiff_{2}(x) = (y_{2} * ((x - x_{1}) * (x - x_{3}) * (x - x_{4}) * (x - x_{5}) * (x - x_{6}) + (x - x_{0}) * (x - x_{3}) * (x - x_{4}) * (x - x_{5}) * (x - x_{6}) + (x - x_{0}) * (x - x_{1}) * (x - x_{4}) * (x - x_{5}) * (x - x_{6}) + (x - x_{0}) * (x - x_{1}) * (x - x_{3}) * (x - x_{5}) * (x - x_{6}) + (x - x_{0}) * (x - x_{1}) * (x - x_{3}) * (x - x_{4}) * (x - x_{6}) + (x - x_{0}) * (x - x_{1}) * (x - x_{3}) * (x - x_{4}) * (x - x_{5}))) / ((x_{2} - x_{0}) * (x_{2} - x_{1}) * (x_{2} - x_{3}) * (x_{2} - x_{4}) * (x_{2} - x_{5}) * (x_{2} - x_{6}))
pdiff_{3}(x) = (y_{3} * ((x - x_{1}) * (x - x_{2}) * (x - x_{4}) * (x - x_{5}) * (x - x_{6}) + (x - x_{0}) * (x - x_{2}) * (x - x_{4}) * (x - x_{5}) * (x - x_{6}) + (x - x_{0}) * (x - x_{1}) * (x - x_{4}) * (x - x_{5}) * (x - x_{6}) + (x - x_{0}) * (x - x_{1}) * (x - x_{2}) * (x - x_{5}) * (x - x_{6}) + (x - x_{0}) * (x - x_{1}) * (x - x_{2}) * (x - x_{4}) * (x - x_{6}) + (x - x_{0}) * (x - x_{1}) * (x - x_{2}) * (x - x_{4}) * (x - x_{5}))) / ((x_{3} - x_{0}) * (x_{3} - x_{1}) * (x_{3} - x_{2}) * (x_{3} - x_{4}) * (x_{3} - x_{5}) * (x_{3} - x_{6}))
pdiff_{4}(x) = (y_{4} * ((x - x_{1}) * (x - x_{2}) * (x - x_{3}) * (x - x_{5}) * (x - x_{6}) + (x - x_{0}) * (x - x_{2}) * (x - x_{3}) * (x - x_{5}) * (x - x_{6}) + (x - x_{0}) * (x - x_{1}) * (x - x_{3}) * (x - x_{5}) * (x - x_{6}) + (x - x_{0}) * (x - x_{1}) * (x - x_{2}) * (x - x_{5}) * (x - x_{6}) + (x - x_{0}) * (x - x_{1}) * (x - x_{2}) * (x - x_{3}) * (x - x_{6}) + (x - x_{0}) * (x - x_{1}) * (x - x_{2}) * (x - x_{3}) * (x - x_{5}))) / ((x_{4} - x_{0}) * (x_{4} - x_{1}) * (x_{4} - x_{2}) * (x_{4} - x_{3}) * (x_{4} - x_{5}) * (x_{4} - x_{6}))
pdiff_{5}(x) = (y_{5} * ((x - x_{1}) * (x - x_{2}) * (x - x_{3}) * (x - x_{4}) * (x - x_{6}) + (x - x_{0}) * (x - x_{2}) * (x - x_{3}) * (x - x_{4}) * (x - x_{6}) + (x - x_{0}) * (x - x_{1}) * (x - x_{3}) * (x - x_{4}) * (x - x_{6}) + (x - x_{0}) * (x - x_{1}) * (x - x_{2}) * (x - x_{4}) * (x - x_{6}) + (x - x_{0}) * (x - x_{1}) * (x - x_{2}) * (x - x_{3}) * (x - x_{6}) + (x - x_{0}) * (x - x_{1}) * (x - x_{2}) * (x - x_{3}) * (x - x_{4}))) / ((x_{5} - x_{0}) * (x_{5} - x_{1}) * (x_{5} - x_{2}) * (x_{5} - x_{3}) * (x_{5} - x_{4}) * (x_{5} - x_{6}))
pdiff_{6}(x) = (y_{6} * ((x - x_{1}) * (x - x_{2}) * (x - x_{3}) * (x - x_{4}) * (x - x_{5}) + (x - x_{0}) * (x - x_{2}) * (x - x_{3}) * (x - x_{4}) * (x - x_{5}) + (x - x_{0}) * (x - x_{1}) * (x - x_{3}) * (x - x_{4}) * (x - x_{5}) + (x - x_{0}) * (x - x_{1}) * (x - x_{2}) * (x - x_{4}) * (x - x_{5}) + (x - x_{0}) * (x - x_{1}) * (x - x_{2}) * (x - x_{3}) * (x - x_{5}) + (x - x_{0}) * (x - x_{1}) * (x - x_{2}) * (x - x_{3}) * (x - x_{4}))) / ((x_{6} - x_{0}) * (x_{6} - x_{1}) * (x_{6} - x_{2}) * (x_{6} - x_{3}) * (x_{6} - x_{4}) * (x_{6} - x_{5}))
pdiff(x) = pdiff_{0}(x) + pdiff_{1}(x) + pdiff_{2}(x) + pdiff_{3}(x) + pdiff_{4}(x) + pdiff_{5}(x) + pdiff_{6}(x)
a = false
b = true
npoints = 7
A = Point(p)
pdiffA: pdiff(x(A))
B: (x(A), pdiffA)
tanlin(x) = y(A) + pdiffA * (x - x(A))
C: (maxx * 0.8, Max[-8, Min[6, tanlin(maxx * 1.05)]])
text1: "slope=" + pdiffA + ""
c = false