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January 30, 2015

January 30, 2015

Posted by **Hannah** on Saturday, February 26, 2011 at 3:46pm.

1)increasing slope for x<4

2) f'(x)>0 for all x(x cannot =4)

3)asymptote at x=4.

Again I know we cannot graph but how can I figure this out?

- Math -
**MathMate**, Saturday, February 26, 2011 at 4:30pmAsymptote at x=4 indicates a factor of (x-4) in the denominator.

Let's try f(x)=1/(x-4)

f'(x)=-1/(x-4)²

so f'(x)<0 for all x except 4.

Let's try f(x)=-1/(x-4)

f'(x)=1/(x-4)² >0 for all x.

Check f"(x)=2/(x-4)³

f"(x)>0 ∀x<4.

So all conditions are satisfied.

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