Implicit Differentiation & Related Rates Review

Given: y = xtany, determine dy/dx.

Consider the curve given by x 2 y – 5xy 2 = -6 Determine the slope of the curve at each point whose y-coordinate is 1. Write the equation of the tangent line at each of these points.

Find the coordinates of the point(s) at which the line tangent to the curve x 3 – xy + y 3 = 0 is horizontal.

Consider the curve given by 3x 2 – 4y 2 = 8. 1) Determine the slope of the curve at the point (2, -1). 2) Is the graph increasing or decreasing at the point (2, -1)? 3) Determine the value of at the point (2, -1). Is the graph concave up or down?

A conical water tank with vertex down has a radius of 10 feet at the top and is 24 feet high. If water flows into the tank at a rate of 20 ft 3 /min., how fast is the radius of the water increasing when the water is 16 feet deep? Include units.

A 10 foot plank is leaning against a wall and is being pushed toward the wall at a rate of ½ feet per second. 1.Find the rate at which the top of the plank is moving up the wall when the bottom of the plank is 8 feet from the wall. Include units. 2.Find the rate at which the angle between the plank and the ground is changing when the bottom of the plank is 8 feet from the wall. Include units.

Assume that oil spilled from a ruptured tanker spreads in a circular pattern whose radius increases at a constant rate of 2 ft/sec. How fast is the area of the spill increasing when the circumference is 120  feet?