1) The coefficient stays on top to make
The rest I don't know
1) if you have 4x^(-2), and you wanted to make the power positive, would you bring the coefficient to the bottom?
e.g. 1/(4x^2) -OR- 4/(x^2)
2) find the derivative of (sqrt(x)-1)/(sqrt(x)+1)
I understand the quotient rule and syntax, it just doesn't work out to the answer that I've been given... PROBABLY a simplification error... here's what I did:
{(x½+1)(1/2x-½)-(x½-1)(1/2x-½)}/(x½+1)^2
(1/2)+(1/2x-½)-(1/2)+(1/2x-½)
x-½/(x½+1)^2
what I get:
1/(x^2(x½+1)^2)
and the answer is 1/(x½(x½+1)^2)
3) why is it that when you look at the cuberoot function (x^(1/3)) from left to right, you see its slope is always positive (albeit undefined at x=0), yet the derivative (1/3x^(-1/3)) shows that its slope is negative from a domain of negative infinity to 0? should it not be positive?
thanks.
Hello, squidplant!
1) if you have , and you wanted to make the power positive,
would you bring the coefficient to the bottom? . . . No
This is correct:
2) Find the derivative of:
I got: . . . . Correrct!
And that becomes: .
You had it right . . . you moved the incorrectly.
3) Why is it that when you look at the cuberoot function from left to right,
you see its slope is always positive (albeit undefined at x=0),
yet the derivative shows that its slope is negative
from a domain of negative infinity to 0? .Should it not be positive?
Your derivative is incorrect: .
So the derivative is positive for all
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
A simple error, but do not be embarrassed.
You are Thinking about derivatives, slopes, signs, increasing/decreasing, etc.
Evidently you have a thorough understanding of these concepts ... impressive!
And you thought you found a contradiction . . . good Thinking!
Thank you very much Sorobon, it's good to know that mathematics still remains my haven of consistency and pure pragmitism with all the things occuring in my life; I owe math a cure for cancer. Take care~
(p.s. i'm in my first year of AP Calculus at my high school, junior year. we're learning integrals in a few weeks! ^_^)