document.write( "Question 727922: A function whose tangent has slope 2x-3 for each value of x passes through the point(0,4).What is the minimum height of the graph \n" ); document.write( "

Algebra.Com's Answer #445343 by KMST(5328) $\"\"$ $\"About$

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That tangent's slope is zero when
\n" ); document.write( " $\"2x-3=0\"$ --> $\"2x=3\"$ --> $\"x=3%2F2\"$
\n" ); document.write( "For $\"x%3C3%2F2\"$ the tangent's slope is negative because $\"2x-3%3C0\"$
\n" ); document.write( "and for $\"x%3E3%2F2\"$ the tangent's slope is positive because $\"2x-3%3E0\"$ .
\n" ); document.write( "That means that the function decreases for $\"x%3C3%2F2\"$ ,
\n" ); document.write( "reaches its minimum value (minimum height of the graph) at $\"highlight%28x=3%2F2%29\"$
\n" ); document.write( "and increases for $\"x%3E3%2F2\"$ .
\n" ); document.write( "There are infinite quadratic functions $\"y=x%5E2-3x%2Bk\"$ whose tangent's slope is $\"2x-3\"$ , but knowing that the graph passes through (0,4) we know that for $\"x=0\"$ {{y=k=4}}} so the function is
\n" ); document.write( " $\"highlight%28y=x%5E2-3x%2B4%29\"$
\n" ); document.write( "However, I do not know how you would know to start with $\"y=x%5E2-3x%2Bk\"$
\n" ); document.write( "because I never had to teach beginning calculus. \n" ); document.write( "

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