document.write( "Question 625894: A. Graph the function ƒ(x) = x3 - 4x + 2.
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\n" ); document.write( "B. Find the domain and range of ƒ, showing all work or explaining your rationale.
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\n" ); document.write( "C. Find the derivative of ƒ, showing all work.
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\n" ); document.write( "D. Find the slope of the graph of ƒ at x = 0, showing all work.
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\n" ); document.write( "E. Let ƒ represent the position of an object with respect to time that is moving along a line. Identify when the object is moving in the positive and negative directions and when the object is at rest, showing all work. \n" ); document.write( "
Algebra.Com's Answer #393860 by Edwin McCravy(20064)\"\" \"About 
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document.write( "A.  Graph the function ƒ(x) = x³ - 4x + 2.\r\n" );
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document.write( "\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx%5E3-4x%2B2%29\"\r\n" );
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document.write( "B.  Find the domain and range of ƒ, showing all work or explaining your rationale.\r\n" );
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document.write( "ƒ(x) is a polynomial function of odd degree.\r\n" );
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document.write( "All polynomial functions are defined for all values of x and have domain\r\n" );
document.write( "(\"-infinity\",\"infinity\")\r\n" );
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document.write( "All odd degree polynomial functions have both domain and range\r\n" );
document.write( "(\"-infinity\",\"infinity\").\r\n" );
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document.write( "C.  Find the derivative of ƒ, showing all work.\r\n" );
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document.write( "ƒ(x) = x³ - 4x + 2\r\n" );
document.write( "ƒ'(x) = 3x² - 4 \r\n" );
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document.write( "D.  Find the slope of the graph of ƒ at x = 0, showing all work.\r\n" );
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document.write( "ƒ(x) = x³ - 4x + 2\r\n" );
document.write( "ƒ'(x) = 3x² - 4 \r\n" );
document.write( "ƒ'(0) = 3(0)² - 4\r\n" );
document.write( "ƒ'(0) = -4\r\n" );
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document.write( "The slope of the graph at x = 0, which is the slope of the \r\n" );
document.write( "green line below which is tangent to the curve at (0,2)\r\n" );
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document.write( "E.  Let ƒ represent the position of an object with respect to time that is moving along a line. Identify when the object is moving in the positive and negative directions and when the object is at rest, showing all work.\r\n" );
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document.write( "ƒ(x) = x³ - 4x + 2\r\n" );
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document.write( "\"d%2F%28dt%29\"f(x) = 3x²\"dx%2F%28dt%29\" - 4\"dx%2F%28dt%29%7D%7D%0D%0A%0D%0A%7B%7B%7Bd%2F%28dt%29\"f(x) = (3x² - 4)\"dx%2F%28dt%29\"}\r\n" );
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document.write( "The object is moving in the positive direction when 3x² - 4 > 0. That is,\r\n" );
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document.write( "Find critical numbers of 3x² - 4 \r\n" );
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document.write( "3x² - 4 = 0\r\n" );
document.write( "    3x² = 4\r\n" );
document.write( "     x² = \"4%2F3\"\r\n" );
document.write( "      x = \"%22%22+%2B-+sqrt%284%2F3%29\"\r\n" );
document.write( "      x = \"%22%22+%2B-+2sqrt%283%29%2F3\"  approximately ±1.1545\r\n" );
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document.write( "These critical numbers are when the object is at rest, because\r\n" );
document.write( "the derivative of f with respect to time is 0 there.\r\n" );
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document.write( "Choose test value -2 which is less that \"-2sqrt%283%29%2F3\"\r\n" );
document.write( "Substitute in 3x² - 4\r\n" );
document.write( "3x² - 4\r\n" );
document.write( "3(-2)² - 4\r\n" );
document.write( "3(4) - 4\r\n" );
document.write( "12 - 4\r\n" );
document.write( "8\r\n" );
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document.write( "That's positive, so the object is moving in the positive direction\r\n" );
document.write( "when x < \"-2sqrt%283%29%2F3\"\r\n" );
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document.write( "Choose test value 0 which is between the two critical numbers\r\n" );
document.write( "\"-2sqrt%283%29%2F3\" and \"2sqrt%283%29%2F3\"\r\n" );
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document.write( "Substitute in 3x² - 4\r\n" );
document.write( "3x² - 4\r\n" );
document.write( "3(0)² - 4\r\n" );
document.write( "-4\r\n" );
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document.write( "That's negative, so the object is moving in the negative direction\r\n" );
document.write( "when \"-2sqrt%283%29%2F3\" < x < \"2sqrt%283%29%2F3\"\r\n" );
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document.write( "Choose test value 22 which is greater that \"2sqrt%283%29%2F3\"\r\n" );
document.write( "Substitute in 3x² - 4\r\n" );
document.write( "3x² - 4\r\n" );
document.write( "3(2)² - 4\r\n" );
document.write( "3(4) - 4\r\n" );
document.write( "12 - 4\r\n" );
document.write( "8\r\n" );
document.write( "That's positive, so the object is moving in the positive direction\r\n" );
document.write( "when x > \"2sqrt%283%29%2F3\"\r\n" );
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document.write( "Answer:  \r\n" );
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document.write( "The object is moving in the positive direction when \r\n" );
document.write( "x < \"-2sqrt%283%29%2F3\" and when x > \"2sqrt%283%29%2F3\"\r\n" );
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document.write( "The object is moving in the negative direction when \r\n" );
document.write( "\"-2sqrt%283%29%2F3\" <  x < \"2sqrt%283%29%2F3\"\r\n" );
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document.write( "The object is at rest when x = \"-2sqrt%283%29%2F3\" and when x = \"2sqrt%283%29%2F3\"\r\n" );
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document.write( "Edwin

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