> 二阶导数描述凹凸性和拐点

Concavity 凹凸性

inflection 拐点

This is a part graph about

Every red line's slop represented as a certain first derivative
.

You can see it clearly that it indeed goes steeper and steeper,
gets bigger and bigger.

That means
keep increasing in this interval.

So according to the first derivative theory,
must be positive.

For a function interval has a feature of
, we call it `concave upwards` (凸).

This is a part graph about

Every red line was becoming more and more gentle,
gets smaller and smaller.

That means
keep decreasing in this interval.

So according to the first derivative theory,
must be negative.

For a function interval has a feature of
, we call it `concave downwards` (凹).

first decreasing , then increasing, you'll get an inflection

first increasing, then decreasing, you'll also get an inflection

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