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We have always known that gradient descent is a function of two or more variables. But how can we geometrically represent gradient descent if it is a function of only one variable?

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For a function of one variable, there are only two options for directions in the domain: left or right, so it becomes almost trivial, but you can still talk about gradient descent.

You would take steps to the left if the slope/derivative is positive and make steps to the right if the slope/derivative is negative--i.e. the opposite direction of the derivative (the 1d version of the "gradient" in gradient descent), which is equivalent to the higher dimensional case.

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"The concept of a direction of fastest descent only makes sense in more than one dimension."

https://math.stackexchange.com/a/180573

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