I need a push in the right direction

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synapsis

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Jan 19, 2006
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I was given a practice exam, and i have run into a series of problems and i have absolutely no idea where to start. Here is the first problem.

Compute and simplify the difference quotient f(x+h) - f(x)/ h h can not = 0

g(x)= 10x^2 +9x -12

the multiple choice answers are

A) 20x +9 +10h B) 20x + 9 C) 20xh +9h +9h^2 D) 10x + 6 +20h


If someone could lay out the correct procedure i would be extremely grateful, i care less if you tell me what the actual answer is- just so i know how to get there is my only concern

thx
 
You are given g(x). That part (the "f(x)" part) is done.

Plug "x + h" in for "x" in the formula for "g(x)". Simplify. Now the "f(x + h)" part is done.

Subtract the first result from the second. Simplify. This gives you g(x + h) - g(x), which is the numerator.

Now divide through by "h". Simplify.

If you get stuck, please reply showing how far you have gotten. Thank you.

Eliz.
 
hx for the help on that first one. It turned out to be just a lot of distribution and simplifying- i got 10x^2 +20xh +10h^2 +9x +9h -12 -10x^2 -9x +12 = 20xh +10h^2 +9h/h= 20x +10h +9 which was the right answer

The next problem i tried to work out and it doesn't work- i'm doing something very wrong. the problem is ...

f(x + h) -f(x)/h h can not be =0

q(x)= 16/x + 28

so what i did was( and i know i'm very wrong because my answer isn't even close)

i plugged in x + h for x so i got 16/(x+h) +28 - 16/ x + 28 for the numerator
the denominator stayed as h

so i thought i would first find a common denominator in the numerator fraction to get rid of the top fraction. So i multiplied the left part by x and the right part by (x+h) and i got
16x/x(x+h) +28 - 16x +16h/x(x+h) +28 for the numerator fraction
the demoninator stays at h

the denominator in the numerator fraction subtracts out, so i get 16x -16x -16h/h
so i get -16h/h =-16 for my final answer :)

the answers to choose from are
A.)15/(x + h +10)(x +10) B.)-15/(x + H + 10)(x +10) C.)-150/(x+h+10)(x+10)
D.)-15/(x+15)^2
 
I know there are some real geniuses in here will someone please help me on the last problem i posted- thank you -the test is tomarrow i really don't have time to wait around hoping for an answer
 
Please post new questions as new topics.

I'll get you started:

\(\displaystyle \L\frac{{f(x + h) - f(x)}}{h}\)

Here, \(\displaystyle f(x) =\L\frac{{16}}{{x + 28}}\) (I can only guess at this line for your question because you are ambiguous. "q(x) = 16/x + 28" is NOT the same as "q(x) = 16/(x + 28)"

Therefore, \(\displaystyle \L\ f(x + h) = \frac{{16}}{{x + h + 28}}\)

Now just put f(x+h) and f(x) in the first equation.

\(\displaystyle \L\left[ {\frac{{16}}{{x + h + 28}} - \frac{{16}}{{x + 28}}} \right]\frac{1}{h}\)

Simplify.
 
I knew how to substitute and set the equation up.
I got where you were at
[16/(x+h+28) -16/(x+28)] but it's not * 1/h it's all over h- if anything it's *h/1 right?

what i was going to attempt to do was to find a common denominator for the fraction above. Honestly i don't know where to go from there because my math doesn't lead me anywhere close to the answers to choose from. the common denominator for the top fraction becomes... what... (x+h+28)(x+28)?

so you would get 16(x+28) -16(x+h+28) over (x+28)(x+h+28) / h or *h/1?
 
synapsis said:
I knew how to substitute and set the equation up.
I got where you were at
[16/(x+h+28) -16/(x+28)] but it's not * 1/h it's all over h- if anything it's *h/1 right?<--------NOPE. That's not right.

what i was going to attempt to do was to find a common denominator for the fraction above. Honestly i don't know where to go from there because my math doesn't lead me anywhere close to the answers to choose from. the common denominator for the top fraction becomes... what... (x+h+28)(x+28)?

so you would get 16(x+28) -16(x+h+28) over (x+28)(x+h+28) / h or *h/1?
Click to expand...

You should remember from grade school arithmetic that dividing by 2 and multiplying by 1/2 give the same result. So, dividing by h and multiplying by 1/h give the same result.

Simplify the expression inside the brackets:

Code: 
16x + 448 - 16x - 16h - 448
--------------------------------
(x + 28)(x + h + 28)

       -16h
-----------------
(x + 28)(x + h + 28)


Now, do the multiplication by 1/h.....

     -16h                 1
----------------    *  -----
(x + 28)(x + h + 28)      h

You can divide out a common factor of "h" from numerator and denominator.

Will this give an answer which resembles one of your choices?
 
I appologize, my teacher is retarted.

Look at the pool of answers to choose from.

A.) 15/(x+h+10)(x+10)
B.)-15/(x+h+10)(x+10)
C.)-150/(x+h+10)(x+10)
D.)-15/(x+15)^2

i appretiate everyones help, i spent time in math lab and the teachers on duty even said they those answers make no sense, it's no wonder i was confused.
 
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