document.write( "Question 25762: Can you please help me with this, we are doing differential Calculus.
\n" ); document.write( "Find the equation of the tangetn for each given x-value.
\n" ); document.write( "y=x^2+8x+12, where x = -4.
\n" ); document.write( "At the back of the book, it says the answer is y=-4
\n" ); document.write( "I have no idea how to get that.
\n" ); document.write( "thank you. \n" ); document.write( "
Algebra.Com's Answer #13861 by josmiceli(19441)\"\" \"About 
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Find the dirivative of y = x^2 + 8x + 12
\n" ); document.write( "It is:
\n" ); document.write( "y' = 2x + 8
\n" ); document.write( "for any value of x, y' will be the slope of the tangent at that point.
\n" ); document.write( "If x = -4, then
\n" ); document.write( "y' = (2 * (-4)) + 8
\n" ); document.write( "y' = -8 + 8 = 0
\n" ); document.write( "so, the slope is 0 when x = -4. When the slope is zero, the tangent to
\n" ); document.write( "the curve is parallel to the x-axis
\n" ); document.write( "What is y when x = -4?
\n" ); document.write( "y = (-4)^2 + 8(-4) + 12
\n" ); document.write( "y = 16 -32 + 12 = -4
\n" ); document.write( "The tangent with 0 slope always takes the form y = f(x)where x is the
\n" ); document.write( "x-coordinate at the point where the slope is 0.
\n" ); document.write( "So, the equation of the tangent is y = -4 \n" ); document.write( "
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