Find the coordinates of points where the graph of f(x) = x4 − 4x3 + 7 has horizontal tangents.

Question

Find the coordinates of points where the graph of f(x) = x⁴ − 4x³ + 7 has horizontal tangents. As a check, graph f(x) and see whether the points you found look as though they have horizontal tangents.

( x , y ) = ( ? , ? ) (larger x-value)

Answer 1

Set the derivative equal to 0: 4x³--12x²=0,,,there is a minimum at x=3.

At x=0, the graph is so steep it is hard to tell exactly what is happening, maybe a point of inflection,,,but apparently not a horizontal tangent.