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Problem 47 Medium Difficulty

If $ g(x) = xf(x), $ where $ f(3) = 4 $ and $ f'(3) = - 2. $ find an equation of the tangent line to the graph of $ g $ at the point where $ x = 3. $

Answer

$y=-2 x+18$

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Video Transcript

Hey, it's clear. So when you read here, so our first gonna use the product roll to find the derivative of G. So it g of X is equal to x times athletics. So the derivative of G it's gonna be equal to that of acts plus x times the derivative of Then we're gonna find too derivative after we plug in three Fergie, the derivative of G of three. And we're gonna use our given values three times the derivative of us of three, which is equal to four plus three times negative too, which is equal to negative, too. So this is gonna be the Slope M of detention line to G of X at X equals three. And we need to find the value for G up three. And we get well, so our line equation why minus y one equals M on X minus X one, and all we do is just plug in, make it why is equal to negative two x plus 18