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Step 4 Substitute any number from the interval into the second derivative and evaluate to determine the concavity. Let me do it in this purple color. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more This graph determines the concavity and inflection points for any function equal to f(x).

For the function \(f(x)=x^3−6x^2+9x+30,\) determine all intervals where \(f\) is concave up and all intervals where \(f\) is concave down. Enter the function you want to differentiate into the Derivative Calculator. (ii) If f'(x) is strictly decreasing on I, then the function is concave down on the open interval I. If your problem involves a specific interval for analysis, specify the interval by providing the lower and upper bounds. Determine the open intervals on which the graph of the function is concave upward or concave downward.

Step 5 Substitute a value from the interval into the derivative to determine if the function is increasing or decreasing. A the first derivative must change its slope (second derivative) in order to double back and cross 0 again. ….

Reader Q&A - also see RECOMMENDED ARTICLES & FAQs. Concave interval calculator. Possible cause: Not clear concave interval calculator.

If f '' changes sign (from positive to negative, or from negative to positive) at some point x = c, then there is an Inflection Point located at x = c on the graph. It occurs when concavity changes. This question asks us to examine the concavity of the function.

If f '' > 0 on an interval, then f is concave up on that interval. The notation for a closed interval is typically of the form [a,b], where a and b are the endpoints of the interval. Concavity; End Behavior; Average Rate of Change; Holes; Piecewise.

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