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Unformatted text preview: ( 2 , 4 ) passes through the point ( 0 , 8 ) . Sketch the curve and tangent line. 7. Examine the function f ( x ) = x + 1 x . (a) Find the points on the curve at which the tangent lines pass through the point ( 1 , 1 ) . (b) Prove that no tangent line to the curve passes through the origin. (c) Prove that there is one tangent line passing though the point ( A,A ) , A 6 = 0 , and it occurs at the point with x-coordinate A 2 . (d) Sketch the curve with a graphing device and illustrate the ideas above. 8. Write a formula for the derivative of each piecewise-dened function. Sketch each curve. (a) f ( x ) = x x x 2 x < (b) f ( x ) = e x x x + 1 x < 9. Write a formula for the n th derivative of the functions: (a) f ( x ) = 1 x (b) f ( x ) = x -...
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