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Problem 66 Hard Difficulty

Let $ \displaystyle F(x) = \int^x_1 f(t) \, dt $, where $ f $ is the function whose graph is shown. Where is $ F $ concave downward?

Answer

$F(x)$ is concave down on the interval $(-1,1)$

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Video Transcript

okay for this question Over here, we know we're trying to figure out where is F Conkey downward? In order to do that, we know we're gonna have to calculate the first and the second derivative. Okay, so given this we know after box is intro from wonder Acts of off of T Do you achieve? Remember, we have the fear of the f Prime of axe is lower case of the vax therefore off Double problem Max is lower case off Problem X Therefore, we know the given graph is decreasing on the interval. Negative 1 to 1. Therefore we know it is Kong Cave down on the interval. Negative 1 to 1.