Animation of secant line converging to tangent line

Coreen Mett, Radford University

f(x) = 1/x

P = (2/3, 3/2)

m[PQ] = (1/(x+H)-1/x)/H

simplified_m[PQ] = -1/((x+H)*x)


Color code: function f(x) in red, secant line in green, tangent line in blue

f ' (2/3) = -9/4 = -2.25

[Maple Plot] [Maple Plot]

Repeat for f(x) = 9 - x^2 at P = (2,5)

  • f(x) = 9-x^2

    P = (2, 5)

    m[PQ] = (-(x+H)^2+x^2)/H

    simplified_m[PQ] = -2*x-H

    [Maple Plot] [Maple Plot]