How to find tangent lines to the inflection pts of a function?

Say we f(x)=x^4 - 6x^3 + 12x^2

f'(x)= 4x^3 - 18x^2 + 24x

f''(x) = 12x^2 - 36x + 24

so the inflection pts are x = 2, x = 1.

Now what do I do to get the tangent lines?

1 Answer

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  • Ray
    Lv 7
    8 years ago
    Favorite Answer

    At points of inflection the gradient of the tangent lines are zero, that is the tangent is a line parallel to the x axis.

    So if we know x = 2 and x = 1 then simply work out f(2) and f(1).

    f(2) = 16

    f(1) = 7

    Thus the tangent lines at the points of inflection are y = 16 and y = 7.

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