A curve in the xy-plane is defined by the equation x^3/3+y^2/2−3x+2y=−1/6. Which of the following statements are true?

i. At points where x=√3, the lines tangent to the curve are horizontal.

ii. At points where x=-2, the lines tangent to the curve are vertical.

iii. The line tangent to the curve at the point (1,1) has slope 2/3.

a) all of them

b) ii and iii

c) i and ii

d) i and iii

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Let C be the curve defined by x^2−y^2=1. Consider all points (x,y) on curve C where x>1 and y>0. Which of the following statements provides a justification for the concavity of the curve?

a) The curve is concave down because y'' = -x/(y^2) < 0

b) The curve is concave down because y'' = -1/(y^3) < 0

c) The curve is concave up because y'' = 1/(y^2) > 0

d) The curve is concave up because y'' = 1/(y^3) > 0