document.write( "Question 296583: find the largest open interval at which function is concave up or concave down and find the location of any points of inflection.\r
\n" ); document.write( "\n" ); document.write( "f(x)= x^4+8x^3-30x^2+24x-3\r
\n" ); document.write( "\n" ); document.write( "Please help with steps \n" ); document.write( "
Algebra.Com's Answer #213688 by stanbon(75887)\"\" \"About 
You can put this solution on YOUR website!
find the largest open interval at which function is concave up or concave down and find the location of any points of inflection.
\n" ); document.write( "f(x)= x^4+8x^3-30x^2+24x-3
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\n" ); document.write( "f'(x) = 4x^3
\n" ); document.write( " + 24x^2 - 60x + 24
\n" ); document.write( "Solve f'(x) = 0
\n" ); document.write( "x = -7.975.. or x = 0.5154 or x = 1.4598
\n" ); document.write( "---
\n" ); document.write( "f\"(x) = 12x^2 + 48x - 60
\n" ); document.write( "Find f\"(-7.975) > 0 so f(x) is concave up in that region
\n" ); document.write( "Find f\"(0.5154) < 0 so f(x) is concave down in that region
\n" ); document.write( "Find f\"(1.4598) > 0 so f(x) is concave up in that region
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\n" ); document.write( "Solve f\"(x)= 0
\n" ); document.write( "x = x = -0.5 or x = 1
\n" ); document.write( "This locates points of inflection.
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\n" ); document.write( "Concave up: (-inf,-0.5)U(1,+inf)
\n" ); document.write( "Concave down: (-0.5,1)
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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