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Draw the graph of a continuous function which is concave downward on $(-1,7),$ decreasing on (-1,5) and increasing on (5,7)

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 3

Concavity and the Second Derivative

Derivatives

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

Boston College

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

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We want to graph a function which is concave down on the interval negative 1-7, decreasing on the interval negative 1-5 and increasing on the interval 5-7. In order to graft dysfunction, we need to have an understanding of how come cavity affects increasing decreasing functions. That is what does it look like for a function to be increasing in conclave? Up decreasing. Concave up and so on. So let's define this visually. Before we proceeded. God, we also know at this point that we're only getting autographs between negative one and seven given the bounds for these two or three requirements. So we have come cavity for coming up and down as related to increasing or decreasing functions here. So highlight in the middle is decreasing functions so concrete up versus down, decreasing functions are given a yellow outside. We see the difference between Conkey down versus up, increasing functions. Therefore we can graph using this information, concave down and decreasing on negative 1 to 5 looks like this as we have here, Concave down and increasing on 5- seven will look like this. Hence this portion

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