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Problem 44 Medium Difficulty

(a) Graph the function $ g(x) = e^x - 3x^2 $ in the viewing rectangle [-1,4] by [-8,8].
(b) Using the graph in part (a) to estimate slopes, make a rough sketch, by hand, of the graph of $ g' $.
(c) Calculate $ g'(x) $ and use this expression, with a graphing device, to graph $ g' $. Compare with your sketch in part (b).


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Video Transcript

it's clear. So when you read here so we have f of facts is equal to eat The axe minus three X squared star graph will look something like this 1234 and then part B We're going to draw another graft this time are derivative And I look like this goes down the X axis and backup and then part see So we're given our original equation and we're gonna differentiate I get Do you ever d x for eat? The X minus three X square is equal to eat the excellent of six acts in the graph Fun. I was down and back up.

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