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Solve the given problems by finding the appropriate derivative.Find the point at which a tangent line to the parabola $y=2 x^{2}-7 x$ is perpendicular to the line $x-3 y=16$

Calculus 1 / AB

Chapter 23

The Derivative

Section 5

Derivatives of Polynomials

Derivatives

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Welcome to enumerate in the current problem we are given a parabolic function with his V equals to two X square minus seven X. Now you also mentioned that there is an author Erika straight line X equals minus three Y 16 with this. But this is how this bill c minus seven X. And supposed this better tangent at that particular point. Now at this point there is another straight line which is uh huh. That's ridiculous. We x minus three Y is equal to 16. So we have to find which is the point at which the stands and we are getting. So in order to get tans and uh calculus problem we take derivatives on both sides. So it is D V D X equals two D D X of two X squared minus seven X. Therefore if we do term by term differentiation it will be D d x of X square minus seven in two D d x of X. That is two and 22 x minus seven into one. Which is four in two x minus seven. So this is the value of the slope of the given equation at any point. Now we are told that the other equation matches up given uh normal to this point will be x minus three. Y is equal to 16. That that is if we take X. Like if we want to go to icicles to mx plus C format then we have x minus 16 is equal to three by that is why is equals two X by three minus 16 by three. That is this would be the value. This is the slope of this equation that is m is equal to one third, correct? Therefore this we always know that the tangent and the normal. Okay, these two will have the multiplication of the slopes would be always one. So if this is one third this should be at that particular point. This should be minus three. Got it. So if we get four X is equal to seven minus three which is four. Therefore we will have X is equal to one close to one. What will be the why did I do correct? We are given Y equals to two X squared minus seven X, correct. So that means two into one square minus seven into one. That is two minus seven minus wipe. So for the given parabola to have tangent at that particular point for which the normal would be x minus three, Y is equal to 16. We will have this intersection point of intersection being one comma minus five. I hope I could explain this problem to you. Let me know if you have integrations.

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