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Find the points at which the graph of the equation has a vertical or horizontal tangent line. 25x2 + y2 - 50x + 10y + 25 = 0 horizontal tangents (x, y) (smaller y-value) (larger y-value) vertical tangents (smaller x-value) (x, y) = ) (larger x-value)
For the limaçon x2 + y2 = (x2 + y2 - 2x)? (Exercise 24 in Section 3.5), verify that the points P(1.0) and 0(3,0) are on the graph and are the rightmost points (tangent line is vertical). (a) plug in x=1, y=0, both sides of the equation are equal to (b) plug in x=3, y=0, both sides of the equation are equal to (c) Find y'at P(1,0): y'I=1.y=0 = (d) Find y' at Q(3,0): y'Ix=3.y=0 =
2. Find the equation of the tangent line to the ellipse z? - zy+y2 = 3 at the point (-1,1). Express your answer in slope-intercept form (y = mz+b).
-y-2x 2+2y de If - 1 + xy + y2 + x2 = 0 and it is known that day find all coordinate points on the curve where x = -1 and the line tangent to the curve is horizontal, or state that no such points exist.
please explain clearly each step Problem statement The graph of the tilted ellipse 2-ry+y2-3 is shown to the right. What are the dimensions and the location of the box containing the ellipse? tangent to the ellipse.
6. Find the equation of the tangent line at the given point. (a) x2 + y2 = 25,(-3, 4) (b) 2y - Vt = 4,(16, 2) (c) y + xy² + 1 = x + 2yº, x = 2
2. Use Definition to find the equation of the tangent line to the graph of the equation y- 1/2 at -2 3. Find the points on the graph of y2-/2 at which the tangent line is parallel to the line y - 3. 4. Sketch the graph of a continuous function f that satisfies all of the stated conditions. f(0) 2, f(-2)- (2)-0, f(-2) f(O)-f'(2)-0 f"(z) > o if-2<zco, f,(z) < 0 if <-2 or x > 0; 2. Use...
Find a normal vector and an equation for the tangent plane to the surface: x3 - y2 - z2 - 2xyz + 6 =0 at the point P : (−2, 1, 3). Determine the equation of the line formed by the intersection of this plane with the plane x = 0. [10 marks] (b) Find the directional derivative of the function F(x, y, z) = 2x /zy2 , at the point P : (1, −1, −2) in the direction of...
4. Tired from the long week, with the amusement park and the wok and dinner plate designs, you retreat to be in peace and study parametric equations. A curious leaflike curve called the "folium of Descartes" catches your eye; it is defined by the parametric equations 3t 3t2 (a) (4 points) Show that if the point (a, b) lies on the curve, then so does (b, a); that is, the curve is symmetric with respect to the line y a....
Find the equation of the tangent line at the point (-3,2) to the curve defined implicitly below. y2 + 3y – 34 = -2x2 + 2x Select the correct answer below: O y = 2z+8 O y = 2x + 4 Oy-1-1 O y=+13 O y=-1-5 O y=x+5