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When the second derivative is positive. In general you can skip the multiplication sign so 5x is equivalent to 5 x.

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We say that a graph is concave up if the line between two points is above the graph or alternatively if the first derivative is increasing.

How to determine concavity. When the slope continually increases the function is concave upward. Taking the second derivative actually tells us if the slope continually increases or decreases. Using this figure here are some points to remember about concavity and inflection points.

And similarly if we re concave upwards that means that our function looks something like this. So if you re concave downwards and you have a point where f prime of let s say a is equal to 0 then we have a maximum point at a. In finance such a curve is said to be convex similarly we say that a graph is concave down if the line between two points is below the graph or alternatively if the first derivative is decreasing.

Sal finds the intervals where g x x 6x 2x 3 is concave down up by finding where its second derivative g is positive negative. Determine the values of the leading coefficient a for which the graph of function f x a x 2 b x c is concave up or down. Solution to example 3 we first find the first and second derivatives of function f.

Plot these numbers on a number line and. Inflection points and concavity calculator. The sections on the.

This is known as the concavety test. A twice differentiable function math f x math is concave up wherever it s second derivative is positive and is concave down wherever it is negative. How to locate intervals of concavity and inflection points find the second derivative of f.

The calculator will find the intervals of concavity and inflection points of the given function. An inflection point occurs wherever the concavety of ma. Determine whether the second derivative is undefined for any x values.

The derivative of a function gives the slope. Analyzing concavity algebraic video khan academy sal finds the intervals where g x x 6x 2x 3 is concave down up by finding where its second derivative g is positive negative. The section of curve between a and b is concave down like an upside down spoon or a frown.

Steps 2 and 3 give you what you could call. When the slope continually decreases the function is concave downward. A positive second derivative means that section is concave up while a negative second.

Set the second derivative equal to zero and solve.