quotient rule problems

[Guest]

hello, I hope you can help me with these two questions:

For this question, : 5.d) Find dy/dx at the given value of x. y=[(x+1)(x+2)]/[(x-1)(x-2)], x=4 To find the the dy/dx, could you expand the brackets and then simplify and then use the quoitient rule, OR would you first use the product rule, then the quoitient rule?

Next question: 8. Show that there are no tangents to the graph of f(x)= 5x+2/(x+2) that have a negative slope. I have no idea on how to do this question.

Thanks very much for the help

 

[galactus]

Your first probelm is equivalent to:

\(\displaystyle \L\\\frac{x^{2}+3x+3}{x^{2}-3x+2}\)

You could try partial fractions. Since the powers of the num. and den. are the same, you would have to long divide first.

After long dividing(one short step), you get:

\(\displaystyle \frac{6x}{x^{2}-3x+2}+1\)

Now try partial fractions if you wish.


You could jump right into the quotient rule:

\(\displaystyle \L\\\frac{(x^{2}-3x+2)(2x+3)-(x^{2}+3x+2)(2x-3)}{(x^{2}-3x+2)^{2}}\)

Looks kinda messy.


For the last problem, differentiate and pay attention to the

denominator of the derivative.