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Sketch the graph of a function which is decreasing to the left of $x=1,$ increasing to its right and passes through (0,-3)

ANSWER IS GRAPH

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 1

Extrema of a Function

Derivatives

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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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This exercise us us to draw the graph of a function that is decreasing to the left of x equals one Increasing to its right and pass through the 0- rate. There are many choices, but here I just use a quadratic function. The function F x echoes X manners one squared minus four. You can verify that it goes across the point their own minus rate And also it is decreasing to the left of articles, one increasing to its rights. The black curve is the graph of a function and right now it is it's derivative, it's derivative as As Prime X. Because two ex miners too, you can verify that the derivative is negative to the left of Mexico's one and positive to its right.

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