document.write( "Question 883389: \"For the function $\"f%28x%29=7x%5E3%2B4x%5E2-3x%2B3\"$ find the maximum number of real zeros that the function can have, the maximum number of x-intercepts that the function can have, and the maxmium number of turning points that the graph of the function can have.\"\r
\n" ); document.write( "\n" ); document.write( "The choices available are: A.3;3;2 B.3;3;3 C. 2;2;1 D. 3;2;1\r
\n" ); document.write( "\n" ); document.write( "using p/q I know that the maximum number of real zeros is 3, so that eliminates choice C, and that the maximum number of x-intercepts is 3. however, I dont know how to find the turning points of the graph. \n" ); document.write( "

Algebra.Com's Answer #533485 by Fombitz(32388) $\"\"$ $\"About$

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Rational root theorem only tells you that if you have real roots, they are rational roots of the form p/q. However they don't tell you anything else about the behavior of the function.
\n" ); document.write( "The maximum number of real zeros that a function can have is equal to the degree of the polynomial. The real zeros and the x-intercept are the same thing so for a cubic polynomial which has degree 3, the maximum number of zeros and intercepts is 3. Similarly the maximum number of turning points is always 1 less than the degree.
\n" ); document.write( "So you're looking for 3,3,2.
\n" ); document.write( " $\"graph%28300%2C300%2C-3%2C3%2C-100%2C100%2C7x%5E3%2B4x%5E2-3x%2B3%29\"$
\n" ); document.write( "In this case, there is only one real root and it is not rational. \r
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