How to show non-negative tangents ?

[ghostanime2001]

Homework Statement

1. Show that there are no tangents to the graph of $$f(x) = \frac{5x+2}{x+2}$$ that have a negative slope.

2. Determine the equation of the tangent to the curve $$y = \frac{x^{2}-1}{3x}$$ at x = 2

Homework Equations

1. Our teacher told us not to use the quotient rule because it is not in our curriculum so please do not give me a solution using the quotient rule. Thanks.

 

[danago]

What about using the product rule with the chain rule then? Use the fact that A/B=AB^-1.

 

[Gib Z]

1. Or Perform Polynomial division on f(x), then its quite simple.

2. You need 3 pieces of information for a tangent - what are they?

 

[ghostanime2001]

for 1. don't i use inequality ? set the equation f(x) < 0 and solve for x if it can't be solved then u can conclude there are no points that can give me a negative tangent

 

[danago]

for 1. don't i use inequality ? set the equation f(x) < 0 and solve for x if it can't be solved then u can conclude there are no points that can give me a negative tangent

If you solve f(x)<0, you will be finding all x for which the function itself is negative i.e. below the x axis. But that's not what you want to find, you need to show that the DERIVATIVE is never negative.