sampleExam.pdf - — Problem 1[3 x 3 Points For the...

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Problem 1 [3 x 3 Points]: For the following functions specify domain and range: a) p | x - 3 | x + 7 , b) x - | x | p x - 3 , c) x 2 - x | x 3 | . Problem 2 [5+5 Points]: Consider the function f ( x ) = ( x - 2) 2 + x on the whole real line. a) Show that f is continuous at x = 0. b) Using the definition of the derivative as the limit of the di erence quotient show that f is di er- entiable and that d dx f ( x ) = d dx (( x - 2) 2 + x ) = 2 x - 3 . Hint: You will not get credit for just applying the rules for di erentiation. You must use the definition of derivative. Problem 3 [3 + 3 Points]: Compute the following derivatives a) d dx p x 3 - 5 x x 2 ! , b) d db p b + 3 ba b 2 - 5 ! . Problem 4 [5 x 4 Points]: Consider the function f ( x ) = 3 2 x 4 + x 3 - 9 x 2 a) Determine domain and range of f . b) Determine where f is monotone increasing and where it is decreasing. c)
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  • Fall '17
  • Tobias Pressuer
  • Calculus

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