document.write( "Question 998629: Find the function f that satisfies the following conditions, f\"(x)=6x+2, f(1)=2, f'(1)=-3\r
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Algebra.Com's Answer #616398 by addingup(3677)\"\" \"About 
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Find the function f that satisfies the following conditions, f\"(x)=6x+2, f(1)=2, f'(1)=-3
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\n" ); document.write( "Solve (d^2 f(x))/(dx^2)= 6 x+2 considering that f(1)= 2 and f'(1)= -3:
\n" ); document.write( "Let's integrate both sides with respect to x:
\n" ); document.write( "(df(x))/(dx)= integral (6x+2)dx= 3x^2+2x+c_1, where c_1 is an arbitrary constant.
\n" ); document.write( "Substitute f'(1)= -3:
\n" ); document.write( "c_1+5= -3
\n" ); document.write( "Solve for c_1:
\n" ); document.write( "c_1= -8
\n" ); document.write( "Substitute the value of c_1:
\n" ); document.write( "(df(x))/(dx)= 3 x^2+2 x-8
\n" ); document.write( "Integrate both sides with respect to x:
\n" ); document.write( "f(x)= integral (3x^2+2x-8)dx= x^3+x^2-8x+c_2, where c_2 is an arbitrary constant.
\n" ); document.write( "Substitute f(1)= 2:
\n" ); document.write( "c_2-6= 2
\n" ); document.write( "Solve for c_2:
\n" ); document.write( "c_2= 8
\n" ); document.write( "Substitute the value of c_2 and we get:
\n" ); document.write( "f(x)= x^3+x^2-8x+8
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