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

## $f^{\prime}(-1)$ is bigger

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##### Catherine R.

Missouri State University

##### Samuel H.

University of Nottingham

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### Video Transcript

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 a dash of x. Right, okay. So here the black hole in this second code 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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