anonymous
  • anonymous
using implicit differentiation find y 'for x2-3xy-4y2=23 and find the equation of the tangent line of the graph at (-1,2)
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
The point of implicit differentiation is to get y' when it isn't possible to get y as a function of x. So, when we implicitly differentiate, we differentiate both sides with respect to x because we want y as a function of x. So: I'm assuming x2 = x² and y2 = y² \[x^{2} - 3xy - 4y^{2} = 23\] \[d/dx(x^{2} - 3xy - 4y^{2})=d/dx(23)\] \[2x - d/dx(3xy) - 8y(dy/dx)=0\] Notice that the middle term is a product rule so and the product rule is the derivative of the first fuction * the second function + the first function * the derivative of the second function. \[d/dx(3xy) = 3y + 3x(dy/dx)\] So the equation is: \[2x - (3y + 3x(dy/dx)) - 8y(dy/dx) = 0\] Simplify: \[2x - 3y - 3x(dy/dx) - 8y(dy/dx) = 0\] \[2x - 3y = (3x + 8y)(dy/dx)\] \[dy/dx = m= (2x - 3y) / (3x + 8y)\] The slope of the tangent line is the derivative so just plug in the point (-1,2) in for x and y in the above equation and then use the same point to get it in y = mx + b form: \[y = (-8/13)x + b\] Now solve this equation for b using the point (-1,2) again and you'll get the equation for the tangent line.

Looking for something else?

Not the answer you are looking for? Search for more explanations.