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Determine where the function is concave upward and downward, and list all inflection points.$$f(x)=x^{4 / 5}-2 x^{3 / 5}$$

Always CU

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 3

Concavity and the Second Derivative

Derivatives

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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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Determine the intervals on…

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Find the intervals on whi…

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Find the intervals on whic…

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question 38 would like to know when f of X equals one minus X to the 3/4 is Khan gave up or down and list all inflection points. So first you need to find the second derivative of F of X, so F prime of X is equal to just negative 3/4. Fax the negative 1/4 taking the second derivative F double Prime of X is equal to 3/16 x, the negative 5/4. So to find an inflection point, that's when F double prime of X is equal to zero. This function never is going to be equal to zero, but it is undefined when X is less than zero. So to test con cavity, we can just test when ex number one X is greater than zero. So taking F double prime of five is equal 2.25 which is positive, which means we are concave up everywhere where X is greater than zero. And that's your answer for question. 38

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