Derivatives 2 Review Derivatives 2 Review Problems Find
Derivatives 2 Review
Derivatives 2 – Review Problems Find if y 2 - 3 xy + x 2 = 7.
Derivatives 2 – Review Problems Find for 2 x 2 + xy + 3 y 2 = 0.
Find if xy 2 - y = x 2. Derivatives 2 – Review Problems Find if xy 2 - y = x 2.
Derivatives 2 – Review Problems Find if y = sin(x + y).
Derivatives 2 – Review Problems Find if x = tan(x + y).
Derivatives 2 – Review Problems Find in terms of x and y: y 3 - xy = 5
Derivatives 2 – Review Problems Find then evaluate the derivative at the point (0, 2): x 2 - 2 xy = y 2 - 4. -1
Derivatives 2 – Review Problems Find then evaluate the derivative at the point (0, 2): x 2 - 2 xy 2 = y 3 - 8.
Derivatives 2 – Review Problems Find then evaluate the derivative at the point (0, 0): 2 x - 5 x 3 y 2 + 4 y = 0.
Derivatives 2 – Review Problems Find then evaluate the derivative at the point (1, -1): x 4 + 4 x 2 y 3 + y 2 = 2 y.
Derivatives 2 – Review Problems Find then evaluate the derivative at the point (0, -2): x 2 - y 2 - 2 x - 4 y - 4 = 0 undefined
Derivatives 2 – Review Problems Determine the slope of the graph of 2 x 2 - 3 xy + y 3 = -1 at the point (2, -3).
Derivatives 2 – Review Problems Find the slope of the line tangent to the graph of 4 y 2 - xy = 3 at the point (-1, -1)
Derivatives 2 – Review Problems Find the slope of the line tangent to the graph of 4 y 2 - xy = 3 at the point
and Derivatives 2 – Review Problems Find the point(s) (if any) of horizontal tangent lines: x 2 + xy + y 2 = 6. and
Derivatives 2 – Review Problems Find an equation of the tangent line to the graph of x 2 + 2 y 2 = 3 at the point (1, 1) x + 2 y = 3
Derivatives 2 – Review Problems Find an equation of the line tangent to the curve x 2 + y 2 = 9 at the point (3, 0) x=3
Derivatives 2 – Review Problems Find an equation of the line tangent to the curve 2 y 2 - x 2 = 1 at the point (7, -5)
Derivatives 2 – Review Problems A machine is rolling a metal cylinder under pressure. The radius of the cylinder is decreasing at a constant rate of 0. 05 inches per second and the volume V is 128π cubic inches. At what rate is the length h changing when the radius r is 1. 8 inches? [Hint: V = pr 2 h] 2. 195 in. /sec
Derivatives 2 – Review Problems As a balloon in the shape of a sphere is being blown up, the volume is increasing at the rate of 4 cubic inches per second. At what rate is the radius increasing when the radius is 1 inch? in. /sec
Derivatives 2 – Review Problems Sand is falling off a conveyor onto a conical pile at the rate of 15 cubic feet per minute. The diameter of the base of the cone is approximately twice the altitude. At what rate is the height of the pile changing when it is 10 feet high? 0. 048 ft/min
Derivatives 2 – Review Problems A point moves along the curve y = 2 x 2 + 1 in such a way that the y value is decreasing at the rate of 2 units per second. At what rate is x changing when Decreasing unit/sec
Derivatives 2 – Review Problems The formula for the volume of a tank is V = πr 3 where r is the radius of the tank. If water is flowing in at the rate of 15 cubic feet per minute, find the rate at which the radius is changing when the radius is 3 feet. ft. / min
Derivatives 2 – Review Problems Air is being pumped into a spherical balloon at a rate of 28 cubic feet per minute. At what rate is the radius changing when the radius is 3 feet? ft. /min
Derivatives 2 – Review Problems Two boats leave the same port at the same time with one boat traveling north at 35 knots per hour and the other boat traveling east at 40 knots per hour. How fast is the distance between the two boats changing after 2 hours? 53. 2 knots/hr
Derivatives 2 – Review Problems The radius of a circle is increasing at the rate of 2 feet per minute. Find the rate at which the area is increasing when the radius is 7 feet. 28π ft 2/min
Derivatives 2 – Review Problems A 5 -meter-long ladder is leaning against the side of a house. The foot of the ladder is pulled away from the house at a rate of 0. 4 m/sec. Determine how fast the top of the ladder is descending when the foot of the ladder is 3 meters from the house. -0. 3 m/sec
Derivatives 2 – Review Problems A metal cube contracts when it is cooled. If the edge of the cube is decreasing at a rate of 0. 2 cm/hr, how fast is the volume changing when the edge is 60 centimeters? -36. 0 cm 3/hr
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