find the difference quotient for f(x) = x^2 + 5x - 5

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marshall1432

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For the function f(x) = x^2 + 5x - 5, find and simplify the difference quotient:

. . .[ f(x) - f(x) ] / [x - 1]

I substituted the phrase for f(x) and for f(1) and got x^2 + 5x - 4. Is there a set of numbers that multiply to give you -4 and add to give you 5? I was looking towards 4 and 1 but + or - wouldnt work. Therefore would the answer be:

. . .[ x^2 + 5x - 4 ] / [x - 1]

Thank you!
 
marshall1432 said:
I substituted the phrase for f(x) and for f(1) and got x^2 + 5x - 4. Is there a set of numbers that multiply to give you -4 and add to give you 5? I was looking towards 4 and 1 but + or - wouldnt work. Therefore would the answer be:[ x^2 + 5x - 4 ] / [x - 1]
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I'm sorry, but I don't understand this paragraph.

To find the difference quotient, first find the pieces.

What is f(x)? Write that down.

What is the value of f(1)? Write that down.

What is f(x) - f(1)? Do the subtraction, and write that down.

Then plug f(x) - f(1) into the difference quotient.

Can the numerator be factored? If so, do either of the factors cancel with the denominator?

Note: You might want to check your arithmetic: -5 - 1 does not equal -4.

Eliz.
 
marshall1432 said:
I substituted the phrase for f(x) and for f(1) and got x^2 + 5x - 4. Is there a set of numbers that multiply to give you -4 and add to give you 5? I was looking towards 4 and 1 but + or - wouldnt work. Therefore would the answer be:[ x^2 + 5x - 4 ] / [x - 1]
Click to expand...
stapel said:
I'm sorry, but I don't understand this paragraph....
Click to expand...
Ok, well let me rephrase it then. I inserted x^2 + 5x - 5 for f(x) and then I already knew that 1 was the value of f(1). therefore the numerator is x^2+5x-5+1 or x^2+5x-4 and the denominator is x-1.

Then for the numerator you have to find 2 numbers that multiply to give you -4 and add to give you +5. I could not find those 2 numbers that did that and to make sure I did it right was the answer x^2+5x-4/x-1 ?
 
i understand that and 2 and 2 doesnt equal 5 either. i was saying that the only possibility to get 4 was through and 5 at the same time is from the numbers 4 and 1. 2 and 2 wouldnt work. Since the answer cant be found by using - or + in front of thoser numbers wouldnt the equation stay like it is? or do you not understand that either?
 
For the function f(x) = x^2 + 5x - 5, find and simplify the difference quotient: .[ f(x) - f(1) ] / [x - 1]
Click to expand...

f(1) = 1, so ...

[f(x) - f(1)]/(x - 1) =

[(x^2 + 5x - 5) - 1]/(x - 1) =

(x^2 + 5x - 6)/(x - 1) =

(x + 6)(x - 1)/(x - 1) =

x + 6
 
thanks, but the problem wasnt the right one. the problem i was having was with:

For the function f(x) = x2 + 5x - 5, find and simplify the difference quotient

f(x)-f(1)/x-1

There ya go.
 
Ummmmm.....please re-read Skeeter's response carefully! That is exactly the problem he did for you!
 
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