The function fails to be differentiable at x = 0. Tell whether the problem is a corner, a cusp, a vertical tangent, or a discontinuity.

y = 3-cuberoot(x)

How would I know how the graph looks like without the use of a calculator?

Question

The function fails to be differentiable at x = 0. Tell whether the problem is a corner, a cusp, a vertical tangent, or a discontinuity.

y = 3-cuberoot(x)

How would I know how the graph looks like without the use of a calculator?

anonymous · Answer

$$ y=3- \sqrt[3]{x}$$

anonymous · Answer

^ Yes. Would the answer be corner?

dumbcow · Answer

its a vertical tangent, the slope is approaching infinity from one end and neg infinity from other end at x=0

anonymous · Answer

Okay, thanks! But my main is question is how can I know what the graph looks like without a graphing calculator? My teacher doesn't allow us to use graphing calculators on our tests, so I need to prepare.