Question about how to start a problem

[elcatracho]

Hello, I am having a bit of trouble understanding how to start a problem that I have been given. This is a summer assignment and I haven't found this symbol in the book or how to use it. SO i was wondering if you could help me. The question is find f(x+ triangle x) for f(x)=x^2-2x-3. The part i don't know how to use is the triangle X part. The symbol is bascially a small triangle beside an x. From past math classes I've known it to mean like differece of. But i'm not sure if that applies here. another question using this same sign is..... Find (f(x+ triangle x) -f(x))/(triangle x) if f(x)=8x^2+ 1. I would really be thankful for some guidance on how to start these two problems and what the symbol means. Thanks, Luis

 

[Guest]

have you learnt about differentiation (dy/dx) ??

 

[elcatracho]

No i don't recall that i have

 

[tkhunny]

The question is find f(x+ triangle x) for f(x)=x^2-2x-3. The part i don't know how to use is the triangle X part. The symbol is bascially a small triangle beside an x. From past math classes I've known it to mean like differece of. But i'm not sure if that applies here.

Your new friend is called "delta". It is very much still the difference, but in this different context "delta-x" it means some small distance in the x direction. Just use what you know of function notation and plug it in. Treat delta-x like a single variable.

If f(x) = x² - 2x - 3,
then f(x+delta-x) = (x+delta-x)² - 2(x+delta-x) - 3

another question using this same sign is..... Find (f(x+ triangle x) -f(x))/(triangle x) if f(x)=8x^2+ 1.

This is almost the same. Simplify as much as possible.

Note: These problems are deliberately designed to prepare you to meet the derivative. I see calculus in your near future. Go without fear.

 

[elcatracho]

The second one still has me thinking

I was able to get the first one no problem... but the second one still has me very confused and i'm getting frusterated with it. i have to find.....
(f(x+deltax)-f(x))/(deltax) if f(x)= 8x^2 +1 This problem is really making me mad and I'd like to finally solve it I'd be very thankful for any assitance on it thanks so much Luis

 

[tkhunny]

Re: The second one still has me thinking

I was able to get the first one no problem... but the second one still has me very confused and i'm getting frusterated with it. i have to find.....
(f(x+deltax)-f(x))/(deltax) if f(x)= 8x^2 +1

So, you're telling me that you can't square a binomial?

f(x) = 8x^2 + 1
f(x+deltax) = 8(x+deltax)^2 + 1 = 8*(x^2 + 2*x*deltax + deltax^2) + 1 = 8*x^2 + 16*x*deltax + 8*deltax^2 + 1

f(x + deltax) - f(x) = (8*x^2 + 16*x*deltax + 8*deltax^2 + 1) - (8x^2 + 1) = 16*x*deltax + 8*deltax^2

[f(x + deltax) - f(x)]/deltax = [16*x*deltax + 8*deltax^2]/deltax = 16*x + 8*deltax