Problem

Find equations of both the tangent lines to the e…

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Problem 75 Hard Difficulty

Find all points on the curve $ x^2 y^2 + xy = 2 $ where the slope of the tangent line is -1.

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Video Transcript

In this problem were given an equation of function and then we are asked to find all the points that the where the slope of tangent line is negative. 1. So, let's first find the slope of tangent line to do the elastic derivative of all the terms with respect to x. We have 2 x times y squared, so we can use product for this torment for the second term 2 x y square plus 2 x. Squared y times y prime plus y plus x times y is equal to 0 point. So from this we see that y prime times 2 x, squared y plus x, is equal to negative of 2 x squared plus y. It means that y prime will be of form negative y times 2 x y plus 1, divided by x times 2 x y plus 1. These will cancel out and we find the derivative to be negative y over x. We want look to be negative 1, so it means that negative y over x will be equal to negative 1 point from this. We see that y then should be equal to x. Now we're going to whenever we see why in the original equation, we're going to apply x and then we're going to solve for x. So let's do that. We have x, squared times x, squared plus x times x is equal to point. This is x square times x. Square plus 1 is equal to 2 point from this we see that x could be 1 or x could be negative. 1 point now using this when x is 1, we see that y is 1, and when i give to the point where the slope of tangent line is negative, 1 are 11 and negative or negative. 1 point.

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Video Transcript

James Stewart

Calculus: Early Transcendentals

Grace He

Catherine Ross

Samuel Hannah

Joseph Lentino

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus: Early Transcendentals

Grace He

Catherine Ross

Samuel Hannah

Joseph Lentino

James StewartCalculus: Early Transcendentals

Grace He

Catherine Ross

Samuel Hannah

Joseph Lentino

James Stewart

Calculus: Early Transcendentals