Unformatted text preview: by x + y 3 = y . (a) Find all points on the curve with xcoordinate . (b) Find the slope of the curve at each point in part (a). (c) How many horizontal tangent lines does the curve have? (d) Find the points on the curve where the slope becomes vertical (vertical tangent lines). (e) Try to sketch the curve using the information above. Then justify your answer by considering that the curve would correspond to the inverse function of portions of y = x 3x . 5. Suppose y is implicitly deﬁned as a function of x by 2 x 2y 2 = 1 . Find the derivative and second derivative with respect to x in terms of x,y . 6. Find the derivative of each function below. (a) f ( x ) = arctan( e x ) (b) f ( x ) = arcsin( √ x ) (c) f ( x ) = arcsin( √ 1x 2 ) (d) f ( x ) = (1 + x 2 ) p arctan( x ) ——————————————————————...
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 Spring '08
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 Calculus, Geometry, Derivative, Mathematical analysis, Continuous function

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