Q: Find y’’ by implicit differentiation. x2 + xy + y2
Find y’’ by implicit differentiation. x2 + xy + y2 = 3
See AnswerQ: (a) The cubic function f (x) = x
(a) The cubic function f (x) = x(x – 2)(x – 6) has three distinct zeros: 0, 2, and 6. Graph f and its tangent lines at the average of each pair of zeros. What do you notice? (b) Suppose the cubic func...
See AnswerQ: For which positive numbers a is it true that ax ≥ 1
For which positive numbers a is it true that ax ≥ 1 + x for all x?
See AnswerQ: Given an ellipse x2/a2 + y2/b2 = 1
Given an ellipse x2/a2 + y2/b2 = 1, where a ≠ b, find the equation of the set of all points from which there are two tangents to the curve whose slopes are (a) reciprocals and (b) negative reciprocals...
See AnswerQ: Find the two points on the curve y = x4 - 2x2
Find the two points on the curve y = x4 - 2x2 - x that have a common tangent line.
See AnswerQ: Suppose that three points on the parabola y = x2 have the
Suppose that three points on the parabola y = x2 have the property that their normal lines intersect at a common point. Show that the sum of their x-coordinates is 0.
See AnswerQ: A lattice point in the plane is a point with integer coordinates
A lattice point in the plane is a point with integer coordinates. Suppose that circles with radius r are drawn using all lattice points as centers. Find the smallest value of r such that any line with...
See AnswerQ: A cone of radius r centimeters and height h centimeters is lowered
A cone of radius r centimeters and height h centimeters is lowered point first at a rate of 1 cm/s into a tall cylinder of radius R centimeters that is partially filled with water. How fast is the wat...
See AnswerQ: A container in the shape of an inverted cone has height 16
A container in the shape of an inverted cone has height 16 cm and radius 5 cm at the top. It is partially filled with a liquid that oozes through the sides at a rate proportional to the area of the co...
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