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Numerade Educator

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Problem 77 Medium Difficulty

For what values of $ a $ and $ b $ is the line $ 2x + y = b $ tangent to the parabola $ y = ax^2 $ when $ x = 2? $

Answer

$$a=-\frac{1}{2} \text { and } b=2$$

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Video Transcript

Hey, we have her equation two x plus y equals B. This becomes why is equal to two x plus Be so we see this is our slope. Why is equal to a X square? And this the derivative becomes too, eh? So the derivative is the slope of detention line. So be negative too when X is equal to so we get a volume of negative 1/2. When we saw b, you just plug it in. We get B is equal to two.