Survey of Calculus Test 2

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  • Topic: Critical point, Stationary point, Function
  • Pages : 13 (1643 words )
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  • Published : March 2, 2013
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Find the x coordinates of all relative extreme points of[pic].

|A)[pic] |B) [pic] |C) [pic] |D) [pic] |E) [pic] |

[pic]

First find the derivative of the function[pic], f ’(x):

|[pic] |= |[pic] |apply power rule of differentiation | | |= |[pic] |simplify | | |= |[pic] |finish simplifying by first factoring | | | | |out GCF | | |= |[pic] |next factor the trinomial factor, | | | | |leaving the final simplified form of | | | | |the derivative |

Set[pic]and solve for x to find critical point(s):

When the derivative is set to zero, [pic]; thus, this implies each factor could be equal to zero, meaning that there could be up to three values for x.

|[pic] |= |[pic] |set first factor equal to zero | |[pic] |= |[pic] |divide each side of the equation by 2| |[pic] |= |[pic] |simplify to find first value of x |

|[pic] |= |[pic] |set second factor equal to zero | |[pic] |= |[pic] |add 3 to each side of the equation | |[pic] |= |[pic] |simplify to find second value of x |

|[pic] |= |[pic] |set third factor equal to zero | |[pic] |= |[pic] |subtract 2 from each side of the | | | | |equation | |[pic] |= |[pic] |simplify to find third value of x |

Therefore, the x-coordinates of the relative extreme points are in the following set: [pic].

|Answer is D |

2) A manufacturer estimates that the profit from producing x units of a commodity is[pic]dollars per week. What is the maximum profit he can realize in one week?

|A) $300 |
|B) $400 |
|C) $500 |
|D) $275 |
|E) none of these |

[pic]

First find the derivative of the profit function[pic], P’(x):

|[pic] |= |[pic] |apply power rule of | | | | |differentiation | | |= |[pic] |simplify |

Set[pic]and solve for x to find critical point(s):

|[pic] |= |[pic]...
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