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Determine where the function is concave upward and downward, and list all inflection points.$$f(x)=4 x^{2}$$

Always CU

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 3

Concavity and the Second Derivative

Derivatives

Missouri State University

Baylor University

Idaho State University

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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Determine where the functi…

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Find the intervals on whic…

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question 22 would like you to determine where f of X equals four X squared is concave upward and downward and list inflection points. So to do so, we need to get this to the second derivative. So F prime of X is equal to eight x and f double Prime of X is equal to 88 here is greater than zero. Therefore, it is concave up. Ah, and the only time would there be an inflection point is when f of X, her F double prime of X is equal to zero. But that is not the case, so it is always Khan gave up, and that's your answer to question 22.

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