document.write( "Question 265306: Find the slope of the tangent line at the given value of x for questions below and then find the equation of the tangent line.\r
\n" ); document.write( "\n" ); document.write( "f(x)=3x^2+x- 2 at x = 1\r
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\n" ); document.write( "\n" ); document.write( "f(x)=(2x^2+1)(x - 1) at x = 3
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Algebra.Com's Answer #195153 by Alan3354(69443)\"\" \"About 
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Find the slope of the tangent line at the given value of x for questions below and then find the equation of the tangent line.
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\n" ); document.write( "f(x)=3x^2+x- 2 at x = 1
\n" ); document.write( "f'(x) = 6x+1
\n" ); document.write( "f'(1) = 7 (slope of tangent)
\n" ); document.write( "f(1) = 2 --> tangent point (1,2)
\n" ); document.write( "y=mx+b
\n" ); document.write( "2 = 7*1+b
\n" ); document.write( "b = -5
\n" ); document.write( "y = 7x - 5 (equation of tangent line)
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\n" ); document.write( "f(x)=(2x^2+1)(x - 1) at x = 3
\n" ); document.write( "f'(x) = 4x(x-1) + 2x^2+1
\n" ); document.write( "f'(x) = 6x^2 - 4x + 1
\n" ); document.write( "At x=3, f' = 43 = slope of tangent line
\n" ); document.write( "f(3) = 38 --> tangent point (3,38)
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\n" ); document.write( "y = mx+b
\n" ); document.write( "38 = 43*3 + b
\n" ); document.write( "b = -91
\n" ); document.write( "--> y = 43x - 91 (eqn of tangent line)
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