2020年11月10日 · Use concavity and inflection points to explain how the sign of the second derivative affects the shape of a function’s graph. Explain the concavity test for a function over an open interval. Explain the relationship between a function and its first and second derivatives. State the second derivative test for local extrema.

The following problems illustrate detailed graphing of functions of one variable using the first and second derivatives. Problems range in difficulty from average to challenging.

Explain the relationship between a function and its first and second derivatives. State the second derivative test for local extrema. Analyze a function and its derivatives to draw its graph. We now know how to determine where a function is increasing or decreasing.

5 天之前 · Apply the First and Second Derivative Tests to determine extrema and points of inflection. We note the signs of f ′ and f ′ ′ in the intervals partitioned by x = ± 1, 0.

2021年7月25日 · Learn how to graph a derivative and how to analyze a derivative graph to find extrema, increasing/decreasing intervals and concavity.

Our definition of concave up and concave down is given in terms of when the first derivative is increasing or decreasing. We can apply the results of the previous section and to find intervals on which a graph is concave up or down.

2012年10月26日 · Here’s a typical graph of a derivative with the first derivative features marked. Here is the same graph with the second derivative features marked. The AP Calculus Exams also ask students to “Justify Your Answer.” The table above, with the columns switched does that.

In this explainer, we will learn how to connect a function to the graphs of its first and second derivatives. The derivatives of a function give us many different techniques for describing the different properties of a curve.

Learning Objectives Explain how the sign of the first derivative affects the shape of a function’s graph. State the first derivative test for critical points. Use concavity and inflection points to explain how the sign of the second derivative affects the shape of a function’s graph.

A tutorial on how to use the first and second derivatives, in calculus, to study the properties of the graphs of functions. To graph functions in calculus we first review several theorem.