document.write( "Question 1155422: Find the critical points of the following function.
\n" ); document.write( "f(x)=2x^2-3x-5 \n" ); document.write( "

Algebra.Com's Answer #778042 by MathLover1(20849) $\"\"$ $\"About$

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\n" ); document.write( "Suppose that x=c is a critical point of $\"f+%28x+%29\"$ .
\n" ); document.write( "If $\"f\"$ ' $\"%28x+%29%3E0+\"$ to the left of $\"x=c\"$ and $\"f\"$ ' $\"%28x+%29%3C0\"$ to the right of $\"x=c\"$ , then $\"x=c\"$ is a local $\"maximum\"$ .
\n" ); document.write( "If $\"f\"$ ' $\"%28x+%29%3C0+\"$ to the left of $\"x=c\"$ and $\"f\"$ ' $\"%28x+%29%3E0\"$ to the right of $\"x=c\"$ , then $\"x=c\"$ is a local $\"minimum\"$ .
\n" ); document.write( "If $\"f\"$ ' $\"%28x+%29\"$ is the $\"same\"$ $\"+sign\"$ on both sides of $\"x=c\"$ then $\"x=c\"$ is neither a local maximum nor a local minimum. \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=2x%5E2-3x-5\"$ .....derivate\r
\n" ); document.write( "\n" ); document.write( " $\"f\"$ ' $\"%28x%29=4x-3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"4x-3=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=3%2F4\"$ -> a critical point: minimum\r
\n" ); document.write( "\n" ); document.write( " domain of $\"f%28x%29\"$ is \r
\n" ); document.write( "\n" ); document.write( "( $\"-infinity\"$ , $\"infinity\"$ )\r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29\"$ is monotone in intervals:\r
\n" ); document.write( "\n" ); document.write( " $\"-infinity%3Cx%3C3%2F4\"$ -> $\"f%28x%29\"$ is decreasing\r
\n" ); document.write( "\n" ); document.write( " $\"3%2F4%3Cx%3Cinfinity\"$ -> $\"f%28x%29\"$ is increasing\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=2%283%2F4%29%5E2-3%283%2F4%29-5\"$
\n" ); document.write( " $\"f%28x%29=2%289%2F16%29-3%283%2F4%29-5\"$
\n" ); document.write( " $\"f%28x%29=%289%2F8%29-%289%2F4%29-5\"$
\n" ); document.write( " $\"f%28x%29=9%2F8-18%2F8-40%2F8\"$
\n" ); document.write( " $\"f%28x%29=-9%2F8-40%2F8\"$
\n" ); document.write( " $\"f%28x%29=-49%2F8\"$ \r
\n" ); document.write( "\n" ); document.write( "minimum is at: ( $\"3%2F4\"$ , $\"-49%2F8\"$ )\r
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