review2f10

# review2f10 - MAC 2311 Test Two Review Fall 2010 Exam covers...

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MAC 2311 Test Two Review, Fall 2010 Exam covers Lectures 11 { 20, Sections 2.7 { 3.7 and 3.9 1. Use the deﬂnition of derivative to ﬂnd a) d dx cos(2 x ), and b) d dx ± 4 p x . 2. Use the deﬂnition of derivative to ﬂnd f 0 ( x ) if f ( x ) = x 3 ¡ 2 x . 3. If f ( x ) = ( 2 ¡ x j x j x < 0 2 + sin x x 0 , ﬂnd the following. For (a) and (b), use limits only. a) Is f ( x ) continuous at x = 0? b) Find f 0 (0) if possible. c) Find an expression for f 0 ( x ). d) Sketch the graph of f ( x ). 4. Indicate whether each of the following statements is true or false. a) If f is continuous at x = a , then f is diﬁerentiable at x = a . b) If f is not continuous at x = a , then f is not diﬁerentiable at x = a . c) If f has a vertical tangent line at x = a , then df dx = 0 at x = a . 5. Suppose that f (4) = 7, g (4) = 2, f ( ¡ 4) = 1, g ( ¡ 4) = 3, f 0 (4) = 10, g 0 (4) = 12, f 0 ( ¡ 4) = 6, and g 0 ( ¡ 5) = ¡ 2. Find: a) h 0 (4) if h ( x ) = g ( f ( x ) ¡ 3 x ) and b) H 0 (4) if H ( x ) = r xf ( x ) + x 2 2 . 6. Find the parabola y = ax 2 + bx whose tangent line at (1 ; 1) is y = 3 x ¡ 2. 7. Find f 0 ( x ) for the following: a) f ( x ) = ( p x ¡ 1) 2 x b) f ( x ) = (6 x ¡ 2) 3 ( x + 4) 2 c) f ( x ) = log 4 ( x cos x ) 2 d) f ( x ) = e x ¡ 3 3 p

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review2f10 - MAC 2311 Test Two Review Fall 2010 Exam covers...

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