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Where Is Concave Downward?

Marcus Vance • • 7 min read
Where Is Concave Downward?

The graph of y = f (x) is concave downward on those intervals where y = f "(x) < 0. If the graph of y = f (x) has a point of inflection

point of inflection
An inflection point is a point on a curve where the curve changes from being concave (going up, then down) to convex (going down, then up), or the other way around. An undulation point is like an inflection point but the type of curve doesn't change.
then y = f "(x) = 0.

What concave downward?

Concavity relates to the rate of change of a function's derivative. A function f is concave up (or upwards) where the derivative f′ is increasing. ... Similarly, f is concave down (or downwards) where the derivative f′ is decreasing (or equivalently, f′′f, start superscript, prime, prime, end superscript is negative).

Where is a function concave down?

A function is concave down if its second derivative is less than 0.

Marcus Vance
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Marcus Vance

Marcus Vance is a cybersecurity auditor and technology writer dedicated to educating the public about online safety, data privacy regulations, enterprise security, and emerging cyber threats.