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Problem 34 Medium Difficulty

For what values of $ x $ does the graph of $ f $ have a horizontal tangent?
$ f(x) = e^x \cos x $

Answer

$\pi / 4+k \pi, \quad k \quad \text{is an integer}$

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Video Transcript

Hey, it's Claire so immune right here. So we're going to look for values of X. We're gonna start with the derivative. It has to be equal to zero. Since the graph of F has a horizontal attention, you have our original function, which is F of X is equal to eat. The X Times CO sign When we derive this, we're gonna eat. Use a product rule. We end up getting co sign terms each X plus e to X terms Negative sign This makes it equal to co sign next term's Eat the eggs, My nest each the X sign We're gonna take out E to the X We get go sign minus sign We make this equal to zero I mean, we end up getting co sign equals sign so X is equal to pi for plus Kate over Cape I. This is because you were using the reference of the unit circle