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Matlab & Mathematica
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Find the critical numbers.and Find the interval(s) where the function, f(x) , is increasing and the interval(s) where it is decreasing.

INSTRUCTIONS TO CANDIDATES
ANSWER ALL QUESTIONS

 

1)  Let f ( x ) = x4/2- 2x3/3- 2x2 + 3


a) Find the derivative.
b) Find the critical numbers. 

 

2)  Giventhat :   f ( x ) = x3 + 9 x2 + 6x - 3

 

  1. Find the critical numbers

  2. Find the interval(s) where the function, f(x) , is increasing and the interval(s) where it is decreasing

 

3)  Let f ( x ) = x2 - 4

  1. Determine the critical number(s).

  2. Determine the absolute extrema on [ 0 , 9 ]

 

4)  Given: f ( x )  =   x  +  9/x + 2

 

  1. Find the critical numbers .

  2. Use the second derivative test to determine local exterema .

 

5) Given  f(x)  = 2x/( x2 + 1 )

  1. Find the derivative

  2. Find the critical numbers

 

6)   f (x) = 2 x2 + 4000/x + 10

 

  1. Find the critical number(s) .

  2. Determine the relative extrema

 

7 )Given:  f ( x )  =  x  +  2 sinx                0 c x c 2u

    1. Find the increasing and decreasing intervals .

    2. Determine relative extrema .

8)        f (x)  =   x  +  2 cos (x)             0  <   x    < 2u

  1. Find the intervals on which f (x) is concave up and concave

  2. Find the inflection point(s) , if any

9 ) If an open box has  square  base  and  a  volume  of  256  in3  and  is  constructed  from a tin Find the dimenstions of  the  box  using  the  least  amount  of material.

10) A private shipping company will accept a box for domestic shipment only if the sum of its length and girth (distance around) does not exceed 96 in. What dimensions will give  a box with a square end the largest possible volume?

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