document.write( "Question 1062776: in the function f(x)=(x-2)^2+4, the minimum value occurs when x is \n" ); document.write( "

Algebra.Com's Answer #677759 by math_helper(2461) $\"\"$ $\"About$

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$\"+f%28x%29+=+%28x-2%29%5E2+%2B+4+\"$
\n" ); document.write( "Take the derivative to get:
\n" ); document.write( "f'(x) = $\"++2%28x-2%29+\"$
\n" ); document.write( "f'(x) = $\"+0+=+2x-4+\"$ —> $\"+x+=+2+\"$ \r
\n" ); document.write( "\n" ); document.write( "x=2 is a critical point (it could be a local minimum, local maximum, or just a flat spot in the function)\r
\n" ); document.write( "\n" ); document.write( "Method 1:
\n" ); document.write( "f(2) = 4
\n" ); document.write( "Also plug in values near x=2, on either side of 2, to see what f(x) does
\n" ); document.write( "f(3) = 5
\n" ); document.write( "f(1) = 5
\n" ); document.write( "—
\n" ); document.write( "Ans: $\"highlight%28+x=2+%29\"$ is where the function's minimum occurs
\n" ); document.write( "(If you are ever given a domain [a,b] of x values, be sure to also compare f(a) and f(b))
\n" ); document.write( "—
\n" ); document.write( "Method 2:
\n" ); document.write( "f'(x) = $\"+2%28x-2%29+=+2x-4+\"$
\n" ); document.write( "Take 2nd derivative and see if function is concave up or down.
\n" ); document.write( "f''(x) = $\"+2+\"$ —> concave up, therefore $\"+highlight%28x=2%29\"$ is where f(x) is minimum\r
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