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The figure shows graphs of $ f $, $ f' $, $ f'' $, and $ f''' $. Identify each curve, and explain your choices.

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$f$ is d, $f^{\prime}$ is $c, f^{\prime \prime}$ is $b,$ and $f^{\prime \prime \prime}$ is a.

04:04

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 8

The Derivative as a Function

Limits

Derivatives

Harvey Mudd College

Idaho State University

Boston College

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

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.

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The figure shows graphs of…

The figure shows the graph…

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Graphical analysis The fig…

in this problem. It is given that the figure shows graphs of F F dash double dash and F double dash identify each girl and explain your choices. Okay, so here we can see A D is the function of if because we can just see one thing in differentiation, what happens is to understand it we will just get into there should be a maximum and minimum points. Right? So maximum and minimum points are found in the CO D. You can see maximum and minimum points. Uh huh. Found in. Mhm Go deep. That means this means D is a function of that function graph Yeah. So, now um what is less than we are just we are just writing in the decreasing order. Right. Mhm. Mhm So now here we have two points. Right, two points. We are getting here for grab. So obviously where we can get f dash request to zero. So there must be two points again. So only two points are available in Kirby cough c so that's right. F dash zero. I'm sorry. This is f dash at dash. We are considering the function graph. Right? So F dash, mm hmm. Shown by graph. Okay, seeing you graph syria Okay. Mhm No, again, if we will differentiate again. So F double dish will be decided. Bye. Mhm Better. The function is one gave up. Yeah. What on game don't Yeah, why? Because this is in graph. See this is decreasing first and it is increasing first. So after differentiation, the graph should increase first, concave up. That is and it should decrease then we can say this uh F dash, double dash, therefore if double dash is represented us. Yeah, graph, uh huh, graphs go B. Sanjay. So moving ahead. Right, we can say the only remaining remaining graph fish E, which is differentiation of triple differentiation of F. Right? So here we can easily write it like this. He is, you can see you this must be written like this, he is nothing. But this is F. Triple dash B is is double dash, no, see is have dash and D is Mhm. Function that that is. So this is how we calculate this graph. Oh, that's good. I hope your industry the concept. Thanks for watching.

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