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Numerade Educator

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Problem 25 Easy Difficulty

(a) Find an equation of the tangent line to the curve
$ y = 2x $ sin $ x $ at the point $ (\pi/2, \pi). $
(b) Illustrate part (a) by graphing the curve and the tangent line on the same screen.

Answer

(a) $$y-\pi=2\left(x-\frac{\pi}{2}\right), \text { or } y=2 x$$
(b)

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Video Transcript

it's clear, so enumerated here. So for part A, we have why is equal to two X sign about? We used the product Fool. I get why the derivative is equal to the derivative of two X I'm sign plus two x who owns the derivative of sign This gives us to sign plus two x co sign Plug in pi over too. Your ex first slope You get two. So using the point slope formula. Yet why minus pi is equal to two times x minus pi over too. Which gives us Why is he called to two sets Next? We're going to go ahead and illustrate it. We have our X and y our original graph. Look something like this. Why? To pine Murray tangents.