Saturday

December 20, 2014

December 20, 2014

Posted by **Krish** on Friday, December 27, 2013 at 2:00pm.

a) Summarize the increasing and decreasing intervals.

b) Compare the slopes of the tangents at the points where i) x=7.5 and x=20

ii) x=6.5 and x=-20

Do it for me please...

- math -
**Damon**, Friday, December 27, 2013 at 2:15pmI have a hunch you actually mean:

g(x)=x/ (x-7)

because that is much more exciting than what you typed.

Now clearly if x = 7 we have a serious problem with this function. It has a zero for its denominator and is therefore undefined at x = 7.

Now what if x = 8 ?

g(8) = 8/1 = 8

And what if x = 6?

g(6) = 6/-1 = -6

Sketch a graph now and watch what is happening

try x = 20

g(20) = 20/13

try x = -20

g(-20) = -20/-27

try x = 100

g(100) = 100/93 humm closer and closer to 1

try x = -100

g(-100) = -100/-107 humm, closer and closer to -1

Now do the x = 7.5 and 6.5 like they said

Now slopes.

You did not say if you know calculus. If not brute force or just use your graph. If you do know then the slope is the derivative at that point so

g'(x) = [(x-7) -x ] / (x-7)^2

or

slope = -7/(x-7)^2

- TYPO - sign error and also note -
**Damon**, Friday, December 27, 2013 at 2:19pmtry x = -100

g(-100) = -100/-107 humm, closer and closer to +1

by the way, notice that the slope is negative everywhere.

**Answer this Question**

**Related Questions**

math - *Consider the function g(x)=x/x-7. a)Summarize the increasing and ...

math - Consider the function g(x)=x/x-7. a) Summarize the increasing and ...

math help please - Consider the function g(x)=x/x-7. a) Determine an equation ...

Calculus - Consider f(x)=200+8x^3+x^4. find the intervals on which function is ...

math-calc - Consider the function f(x)= (2x+8)/(6x+3). For this function there ...

math - . Given the following function, f(x)=-x^2 -8x find: (a) vertex, (b) axis...

Engineering Calculus - f(x)=((6x-3)/(x+6)) how do you find the intervals of ...

Calculus - Consider the function f(x)=-2x^3+33x^2-108x+2. For this function, ...

Calculus - find the intervals where the function is increasing and the intervals...

Calculus - Consider the function f(x) = x - lnx. Find the intervals on which f(x...