document.write( "Question 535051: Find the value of f(2) when f,g are differentiable functions such that (fg)′(x) = f(x)g′(x), g(x)<0, for all x, while f(0) = 4 \n" ); document.write( "

Algebra.Com's Answer #351958 by richard1234(7193) $\"\"$ $\"About$

You can put this solution on YOUR website!
The product rule says that\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If this is equal to f(x)g'(x), then\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since g(x) cannot equal 0, then f'(x) = 0 for all x, then f(x) is a constant function. Since f(0) = 4, then f(2) is also equal to 4. \n" ); document.write( "

\n" );