Yes, the concavity of a curve can be determined by differentiation. To find out the concavity of a graph at various points, you want to analyze the second derivative (f''(x)). Take the derivative of your original equation, then, take the derivative of this equation. By setting this second derivative to zero, you can solve for the critical points (x-intercepts/asymptotes) of the second derivative graph. Once these critical points are found, make a number line with these points marked. By doing a sign test on either sides of the critical points (plug in numbers below and above the critical points into the second derivative equation), you can find the concavities of your original graph. Wherever the sign tests results in a positive number, that is where a upward facing curve is (concave up); where it is negative, that is where a concave down portion is.
Chat with our AI personalities
An inflection point is a point on a curve at which the sign of the curvature (i.e., the concavity) changes.
Yes. For example, consider a standard normal curve. z = 1 and z = -1 happen to lie at the inflection points of the normal curve.
You find the gradient of the curve using differentiation. The answer is 0.07111... (repeating).
of, pertaining to, or determined by regression analysis: regression curve; regression equation. dictionary.com
I can describe the shape of a kidney as an oval with a concavity in one side.