document.write( "Question 858241: Hello, I am working through my application of derivatives assignment and have come across a question I kind of understand but am unsure if I should use my method, any help would be highly appreciated:\r
\n" ); document.write( "\n" ); document.write( "The base b, and height, h, of a Triangle are represented by b= (t+3)^2 and
\n" ); document.write( "h= t^2+3. Determine the rate of change of the area of the triangle when t=3.\r
\n" ); document.write( "\n" ); document.write( "By my understanding, am I supposed to find b'(3) and t'(3)?
\n" ); document.write( "I do not understand how to fit in Area into this question\r
\n" ); document.write( "\n" ); document.write( "Any help would be much appreciated
\n" ); document.write( "Thank You \n" ); document.write( "
Algebra.Com's Answer #517158 by rothauserc(4718)\"\" \"About 
You can put this solution on YOUR website!
we are given b= (t+3)^2 and h= t^2+3
\n" ); document.write( "Area of triangle is 1/2 * b * h
\n" ); document.write( "therefore
\n" ); document.write( "A = (1/2) * (t+3)^2 * (t^2+3)
\n" ); document.write( "A = (1/2) * (t^2+6t+9) * (t^2+3)
\n" ); document.write( "A = (1/2) * (t^4 + 6t^3 + 12t^2 + 18t + 27)
\n" ); document.write( "A = t^4/2 + 3t^3 + 6t^2 + 9t + 27/2
\n" ); document.write( "now
\n" ); document.write( "dA/dt = 2t^3 + 9t^2 + 12t + 9
\n" ); document.write( "for t = 3
\n" ); document.write( "dA/dt = 2*27 + 9*9 + 36 + 9 = 180\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );