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A function with a horizontal tangent at a point but no change from increasing/decreasing...?
Give an example of how a function can have a horizontal tangent at a point but no change from increasing/decreasing or vice versa at that point. Show the first derivative chart.
Please help explain. Thanks.
1 Answer
- Pi R SquaredLv 71 decade agoFavorite Answer
Hi,
y = x³
The first derivative is f'(x) = 3x².
When x = 0, y = 0, and the slope is 3x² = 3(0)² = 0.
The graph is increasing but this point is a point of inflection where the tangent is 0.
x . slope
--------------
-2 . . 12
-1 . . 3
0 . . 0 <=horizontal slope
.1 . . 3
2 . .12
I hope that helps!! :-)
