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

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

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Missouri State University

Campbell University

Oregon State University

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.