1 min readβ’january 22, 2021

Sumi Vora

If we look at the first derivative of a function, we can see that if the rate of change of the function is increasing on an interval, the function is **concave up**. Likewise, if the rate of change of the function is decreasing, the function is **concave down**.Β

We can determine whether the first derivative is increasing or decreasing by taking the derivative of the derivative (aka the **second derivative**).Β π΅

If f"(a) = 0, then c is a special point called a **point of inflection**, which occurs when the function switches concavity. At a point of inflection, f(x) is neither concave up or concave down; it is linear at that point.Β π‘

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