In the solution of the Worked Example of Differentiation: Part A: Session 2
It's written:
"Our intuition about the tangent line tells us that any line tangent to the graph at (0, 0) must
go through (0, 0) and then “follow the direction of the graph” near (0, 0)."
What does it mean that the tangent must follow the direction of the graph ?? How could the tangent line follow both directions of the graph ??

Question

In the solution of the Worked Example of Differentiation: Part A: Session 2
It's written:
"Our intuition about the tangent line tells us that any line tangent to the graph at (0, 0) must
go through (0, 0) and then “follow the direction of the graph” near (0, 0)."
What does it mean that the tangent must follow the direction of the graph ?? How could the tangent line follow both directions of the graph ??

phi · Answer

The idea is we have a "smooth curve"  (no sharp turns, no gaps)
The tangent line to the curve at some point looks like this (for example)
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