Can anyone tell me what this is so I can try to figure out how to do it.

[hopelynnwelch]

Not looking for an answer just a term to search to refresh myself on how to solve these again. It has been a long time!

Evaluate:

f(1+h)-f(1) / h

for f(x)=x^2-2x

TIA!

 

[wjm11]

Not looking for an answer just a term to search to refresh myself on how to solve these again. It has been a long time!

Evaluate:

f(1+h)-f(1) / h

for f(x)=x^2-2x

TIA!

The term you are looking for is "derivative." Take a look here (or many other places):

http://en.wikipedia.org/wiki/Derivative

Check out the example...

 

[stapel]

Not looking for an answer just a term to search to refresh myself on how to solve these again. It has been a long time!

Evaluate:

f(1+h)-f(1) / h

for f(x)=x^2-2x

This is just "operations" on functions. This particular format is something you'll see again once you get to calculus; it will be used to introduce the "derivative". But you're not taking limits; you're not fiddling with infinity. You're just evaluating.

Evaluate f(1). Evaluate f(1 + h). Subtract the former from the latter. Simplify the result. Then divide by h. Simplify. That's it.

 

[HallsofIvy]

Not looking for an answer just a term to search to refresh myself on how to solve these again. It has been a long time!

Evaluate:

f(1+h)-f(1) / h

Do you mean "(f(1+h)- f(1))/h"? The parentheses are important!

for f(x)=x^2-2x

TIA!

The term would be "difference quotient" which is used in the definition of the derivative.

You are told that f(x)= x^2- 2x. So what is f(1)? What is f(1+h)?

 

[hopelynnwelch]

You are correct, the parenthesis do matter. I meant:

[f(1+h)-f(1)] / h

So this is in essence what they want?

[ ((1+h)^2-2(1+h)) ] - [ (1^2-2(1)) ] / h

Then "subtract the former from the latter. Simplify the result. Then divide by h. Simplify."

To get:

[ (1+h)^2-h-1] / h

And then:

(1+h)^2 / h - h/h - 1/h

Or:

(1+h)^2 / h - 1 - 1/h

 

[Ishuda]

You are correct, the parenthesis do matter. I meant:

[f(1+h)-f(1)] / h

So this is in essence what they want?

[ ((1+h)^2-2(1+h)) ] - [ (1^2-2(1)) ] / h

Then "subtract the former from the latter. Simplify the result. Then divide by h. Simplify."

To get:

[ (1+h)^2-2h-1] / h <== fix your mistake and continue

And then:

(1+h)^2 / h - h/h - 1/h

Or:

(1+h)^2 / h - 1 - 1/h

See your mistake above.

 

[hopelynnwelch]

Ahh yes! I did mess up!

Answer:

(1+h)^2/h - 1/h - 2

Thank you!

 

[Steven G]

Ahh yes! I did mess up!

Answer:

(1+h)^2/h - 1/h - 2

Thank you!

[ ((1+h)^2-2(1+h)) ] - [ (1^2-2(1)) ] / h =[1+2h+h^2-2-2h+1]/h =[h^2]/h =h

 

[hopelynnwelch]

[ ((1+h)^2-2(1+h)) ] - [ (1^2-2(1)) ] / h =[1+2h+h^2-2-2h+1]/h =[h^2]/h =h

Really? I need to square the term and keep it going? OK...

 

[Steven G]

Really? I need to square the term and keep it going? OK...

Isn't my answer of just h much cleaner that your answer? Yes, you should square and then combine like terms.