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The graphs of a function $ f $ and its derivative $ f' $ are shown. Which is bigger, $ f'(-1) $ or $ f''(1) $?

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03:08

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 8

The Derivative as a Function

Limits

Derivatives

Campbell University

Oregon State University

Baylor University

University of Nottingham

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 graphs of a function $…

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One of the graphs shown is…

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Gives a formula for a func…

in this problem, the graphs of the function F n is celebrated with Daschle show which is bigger. Ev dash minus one or F double dash one. So for two graphs, it is us that which one is bigger? So we can see in craft one we are given with red and black coffee. Right? So read a read of cough shows us the maximum. So that's why it will be F dash of X already. So we can easily say this is off. This is a dash X. Okay. Now, simply again moving to the another graph, we are just identified which is which is F X and bridges air dash of X. Right, okay. So here the black hole in the second call we can see the black up is showing maximum. Right? So this will be F dash X and red gold will be fx All right, so first step is over now. Now for the second step we are taking the first first problem first. Well, yeah, F- -1. F- -1 is less than zero. Yeah, So F- -1. That is F- -1 is zero year. Okay, You can see here this is -1. Right? So this will be zero here. This is less than zero. You can see uh I'm sorry, this should be here. Okay, here it should be my next one. Right? So it should be less than zero year. Why? Because the Y value is in the negative part. You can see here. Right, So that's why we are taking uh less than zero. So this is we are talking about the value for why that's why fx is represented for the wife. So X. Is the value for the X and y will be the value for fX trade or FDA checks. You can see. So here we can easily say that in this graph we can see this graph is going downwards that means it has the value less than zero. Now for F dash of X right at X is equal to one. So now after sex, F dash eggs At x equals two. What? So here we can see the slope is zero year. Right? So that's why this F D double dash one is greater than a dash of minus one year. Now for the second question we can see here F- -1 is greater than zero. Have dash minus one is greater than zero. So here is the value and we are getting the black one in the upper side. So that will be the positive value. That is greater than zero value in the by excess. Can we see here this is positive and this is this is actually negative. Right, negative bending. Okay, so here when we put F double-1 mhm Right equals to zero. So it becomes equals true zero. Yeah, he Right. So this is this is the way we can conclude that F- -1 is later than f double dash of one. So remember this low fall. Remember the slope slope is equal to zero at f d s X when x is equal to one year. Can we see you? Yes, We can see you at if one this little busy real? Okay, so this is why we have got this answer. I hope you understood the concept. Thanks for watching.

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