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Unformatted text preview: f (2) =3 and f 00 ( x ) < 0 for all x then (a) f (1) < 10. (b) f (1) = 10. (c) f (1) > 10. (d) there is not enough information to say anything about f (1). If f ( ω ) = e 3 π 100 then f ( ω ) is (a) e 3 π 100 . (b) 3 e 2 π 100 . (c) 100 e 3 π 99 . (d) 300 e 2 π 99 . (e) e 3 π 100 + 100 e 3 π 99 . (f) 3 e 2 π 100 + 100 e 3 π 99 . (g) none of the above. If f ( r ) = cosh(2 r ) then f (101) (0) (i.e., the 101st derivative evaluated at 0) is (a)2 101 (b) 0 (c) 1 (d) 2 101 (e) none of the above. 5. Find the derivatives of the following functions (hint: it might be possible to simplify the function before taking the derivative): (a) (5 points) f ( x ) = cos 2 ( x 2 ) + tan 2 ( x 2 ) + sin 2 ( x 2 ) (b) (4 points) f ( x ) = y 42 y 2 + 1019 y + 3 y 6. (8 points) Find an expression for dy dx (i.e., dy dx = something involving y and/or x ) given that x + y = arctan( y ) ....
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 Spring '07
 Arnold
 Calculus, Derivative, Convex function

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