document.write( "Question 1038078: A1. Find an example of a function f such that:
\n" ); document.write( "-the line y = 2 is a horizontal asymptote of the curve y = f(x), and
\n" ); document.write( "-the cures intersects the line y = 2 at an innite number of points.
\n" ); document.write( "Note: For full marks, prove that lim x->1 f(x) = 2, find all intersection points, and sketch a graph of the curve and the line y = 2. \r
\n" ); document.write( "\n" ); document.write( "A2. Let f(x) = x3 - bx for some real number b.
\n" ); document.write( "a. Find f(x) using the limit definition of the derivative.
\n" ); document.write( "b. If the curve y = f(x) has a horizontal tangent line at a point with x = 2 find the
\n" ); document.write( "y-coordinate of this point. (Your answer should be a real number, not an expression
\n" ); document.write( "involving b.) \r
\n" ); document.write( "\n" ); document.write( "Been struggling with these 2 questions...Thankyou \n" ); document.write( "

Algebra.Com's Answer #652848 by Boreal(15235) $\"\"$ $\"About$

You can put this solution on YOUR website!
Here is the second one.
\n" ); document.write( "y=x^3-bx
\n" ); document.write( "f(x+h)-f(x)/h
\n" ); document.write( "numerator=(x+h)^3-x^3=x^3+3x^2h+3xh^2+h^3-b(x+h)-x^3-bx
\n" ); document.write( "This is 3x^2h+3xh^2+h^3-bx-bh-bx=3x^2h+3xh^2+h^3-bh
\n" ); document.write( "Divide that by h
\n" ); document.write( "=3x^2+3xh+h^2-b
\n" ); document.write( "as h goes to 0, f'(x^3) goes to 3x^2-b, which is the derivative.
\n" ); document.write( "f(x) when x=2 is 8-2b
\n" ); document.write( "The derivative must equal zero, so 3x^2-b=0 for x=2. Therefore b=12
\n" ); document.write( "the y-coordinate of the point when x=2 is 8-24 or -16. The point is (2,-16)
\n" ); document.write( " $\"graph%28300%2C200%2C-10%2C10%2C-30%2C30%2Cx%5E3-12x%2C-16%29\"$ \r
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