Gradient of line parallel to y-axis

Hi guys... one quick question...
If a curve has a point A...
The tangent to point A is parallel to the y-axis...
Is the gradient of this tangent 0?...Will it be like a turning/stationary point?...

Reply 1

dvs

10

If it's parallel to the y-axis, then it's of the form x=a, so it has no gradient (or it has an infinite gradient, since you're basically considering gradient=tan(pi/2)). Moreover, if a curve has a tangent that is parallel to the y-axis, then it can't be a graph of a function. (Think "horizontal line test.")

Reply 2

Chewwy

17

dvs

If it's parallel to the y-axis, then it's of the form x=a, so it has no gradient (or it has an infinite gradient, since you're basically considering gradient=tan(pi/2)). Moreover, if a curve has a tangent that is parallel to the y-axis, then it can't be a graph of a function. (Think "horizontal line test.")

don't you mean vertical line test? besides, what about, say, f(x) = x^1/3 ?

Reply 3

laith.aleissa

3

Lol some late reply but it Basically means that Dy/Dx doesn't exist for that point.
Therefore Dy/Dx =f(x)/g(x), say that was your dy/dx g(x)=0 if the a point is parallel to the y axis. also if parallel to the x axis then f(x)=o, dy/dx=0.

Gradient of line parallel to y-axis

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