PROBLEM #1 (NO CALCULATOR) Consider the curve xy-xy=1 1 Use implicit differentiation to show that 2...

Transcribed Image Text:

PROBLEM #1 (NO CALCULATOR) Consider the curve xy-xy=1 1 Use implicit differentiation to show that 2 dy y(3x-2) dy_y = dx x(1-x) Find the equation of all horizontal tangent lines. 3 Find the equation of all vertical tangent lines. 4 6 Find the equation of the tangent line(s) at x=2. Using the tangent line at x=2, approximate y(2.1). 1 Is the curve increasing or decreasing at x == ? Justify your answer. 2 7 1 Is the curve concave up or down at x== ? Justify your answer. 2 8 Would a tangent line approximation overestimate or underestimate at x=? Why? 2 PROBLEM #1 (NO CALCULATOR) Consider the curve xy-xy=1 1 Use implicit differentiation to show that 2 dy y(3x-2) dy_y = dx x(1-x) Find the equation of all horizontal tangent lines. 3 Find the equation of all vertical tangent lines. 4 6 Find the equation of the tangent line(s) at x=2. Using the tangent line at x=2, approximate y(2.1). 1 Is the curve increasing or decreasing at x == ? Justify your answer. 2 7 1 Is the curve concave up or down at x== ? Justify your answer. 2 8 Would a tangent line approximation overestimate or underestimate at x=? Why? 2