Is the x-axis tangent to $y = x^3$ ?

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Answer 1 · 2018-03-08T06:04:07

Since the slope of the curve is zero at $x=0$ where the curve
cuts the x-axis, x-axis is tangent to the given curve.

Given =

$y=x^3$

This curve passes through origin $x=0$ .
The slope of the X-axis is zero.

The slope of the given curve at any point is $dy/dx=3x^2$

The slope of the curve at $x=0$ is $m=3(0)^2=0$

Since the slope of the curve is zero at $x=0$ where the curve
cuts the x-axis, x-axis is tangent to the given curve.

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Is the x-axis tangent to y = x^3y = x^3?