WebThe graph consists of a curve. The curve starts in quadrant 2, moves downward concave up to the y-axis, moves upward concave up through 2 points, and ends in quadrant 1. Tangent lines move upward and touch each of the 2 points. The line tangent to the higher point, at a higher x-value, has a steeper slope than the line tangent to the lower point. WebSal introduces the concept of concavity, what it means for a graph to be "concave up" or "concave down," and how this relates to the second derivative of a function. Created by Sal Khan. Sort by: ... I wish you had …
Determining Intervals of Concavity and Inflection Points
WebThe definition of the concavity of a graph is introduced along with inflection points. Examples, with detailed solutions, are used to clarify the concept of concavity. Example 1: Concavity Up Let us consider the graph below. … WebThat means as one looks at a concave down graph from left to right, the slopes of the tangent lines will be decreasing. Consider Figure 3.4.3, where a concave down graph … shoes with black dress and tights
Concavity intro (practice) Concavity Khan Academy
WebTranscribed Image Text: (a) Find a function f that has y = 4 – 3x as a tangent line and whose derivative is equal to ƒ' (x) = x² + 4x + 1. (b) Find the area under the curve for f (x) = x³ on [−1, 1]. e2t - 2 (c) Determine where the function is f (x) = cos (t²-1) + 3 (d) Express ² sin (x²) dx as limits of Riemann sums, using the right ... WebAs you move from left to right, the slope of the tangent line decreases. The slope of the tangent line is given by , and to say something decreases means its derivative is … WebDec 20, 2024 · Figure \(\PageIndex{3}\): Demonstrating the 4 ways that concavity interacts with increasing/decreasing, along with the relationships with the first and second … shoes with bubble soles