Problem

(a) The curve with equation $ y^2 = x^3 + 3x^2 $…

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Problem 33 Medium Difficulty

(a) The curve with equation $ y^2 = 5x^4 - x^2 $ is called a kampyle of Eudoxus. Find an equation of the tangent line to this curve at the point (1, 2).
(b) Illustrate part (a) by graphing the curve and the tangent line on a common screen. (If your graphing device will graph implicitly defined curves, then use that capability. If not. you can still graph this curve by graphing its upper and lower halves separately.)

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Video Transcript

In this problem were given a curve we are asked to find in part a the equation of tangent line at .12 in part, were asked to plot on the same graph, the function itself and the derivative of that function. So we know that tangent line will be from y. Minus y is equal to derivative, a given point x and multiplied by x, minus x, and so let's find derivative function. First, let's take derivative on both sides. We have 2 y times y prime, is equal to 20 x cubed minus 2 x. We know x, not a 1 that is given, so we can find what am at a given point plus pluck the given values, and so we have 4 times what prime is equal to 20 minus 2, and that is 18 from this. We can see that y prime will be 9 over 2 point all right if y prime is 9 over 2 point. It is this term we can find the equation of 10 lines. Y minus 2 is equal to 9 over 2 x. Minus 1 from the standard equation is 9 x over 2 minus 5, o 2 point now in part b, you can use any ling bunch of plotter or even your calculators. This is what we have. The function looks like this is our function itself y, and here is our point so 2, that is y axis, and that is the x axis, and this is the derivative of this function y prime- and that is the tangent point right here.

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Problem

(a) The curve with equation $ y^2 = x^3 + 3x^2 $…

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Video Transcript

James Stewart

Calculus: Early Transcendentals

Heather Zimmers

Kayleah Tsai

Caleb Elmore

Joseph Lentino

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

Calculus: Early Transcendentals

Heather Zimmers

Kayleah Tsai

Caleb Elmore

Joseph Lentino

James StewartCalculus: Early Transcendentals

Heather Zimmers

Kayleah Tsai

Caleb Elmore

Joseph Lentino

James Stewart

Calculus: Early Transcendentals