derivitive help

[Zerrotolerance]

Hello,

I'm really struggling with two math problems I can't figure out. I would appreciate any help or tips. If anyone can help, please don't give me the answer without explaining how you found it, so I know what to do.

The first is:

Consider the curve y = x - x[sup:3cnxq58c]2[/sup:3cnxq58c].
(a) Find the slope of the tangent line to the curve at the point (1, 0).

Now i thought F(a) = 0 and F(x)= x-x[sup:3cnxq58c]2[/sup:3cnxq58c]

So, I need to find the slope by finding the limit as x approahes 0 of F(x)-f(a)/x-a.

so,

((x-x[sup:3cnxq58c]2[/sup:3cnxq58c])-0)/x-a = ((0-0[sup:3cnxq58c]2[/sup:3cnxq58c])-0)/x-1= 0/0=0

m=0

b)then it asks to find the equation of the line which I could do if I could find the right slope. I can do many other problems like this, but seem to be struggling with this one for some reason.

The second problem is:

sqr = squareroot

((sqr(x) - sqr(x+h))/(h(sqr(x)(sqr(x+h))) = the squareroot of X minus the squareroot of X+H, all divided by H times the squareroot of X times the squareroot of X+H.

Rationalize the numerator.

Any help would be appreciated. Thank you!

 

[galactus]

Consider the curve y = x - x[sup:30aycfgz]2[/sup:30aycfgz].
(a) Find the slope of the tangent line to the curve at the point (1, 0).

Find the derivative of \(\displaystyle x-x^{2}\) and sub in x=1. That is the slope, m, at that point.

Then, along with m just found, sub x=1 and y=0 into y=mx+b and solve for b. You're done.

This answers the next question as well.

 

[Zerrotolerance]

Well, I already froze out the first one. I was doing problems that seemed like they were 100 times harder and getting them all right, but I couldn't get that one to work. I am still having trouble with the rationalizing the square root one, does anyone know the answer to this. I am on my last guess. I have tried everything I can think of and it's due in 2 hours.

answers I've tried include

-1/(2sqr(x))

-1/(2x(sqr(x)))

-1/(sqr(x)(sqr(x+h)))

I haven't tried

-1/(x(sqr(h)) or -1/x

These are my last two guess, but I don't want to lose the points by guessing wrong. Thanks!

 

[Deleted member 4993]

Hello,

The second problem is:

sqr = squareroot

((sqr(x) - sqr(x+h))/(h(sqr(x)(sqr(x+h))) = the squareroot of X minus the squareroot of X+H, all divided by H times the squareroot of X times the squareroot of X+H.

Rationalize the numerator.

Any help would be appreciated. Thank you!

To rationalize the numerator of:

\(\displaystyle \frac{\sqrt{x} \ - \ \sqrt{x-h}}{h\sqrt{x}\sqrt{x-h}}\)

Multiply both numerator and the denominator by:

\(\displaystyle \sqrt{x} \ + \ \sqrt{x-h}\)

 

[Zerrotolerance]

I did that, but all my answers were wrong. I included a list of the ones that i tried. I don't know if I'm not doing the denominator correctly or if I am trying to simplify it too much. I hate the site we use because it is very picky about what it wants. Even if it's the right answer it likes it a certain way. ah..well..another one wrong.

 

[mmm4444bot]

I did that

You did what ?

Subhotosh typed x - h and you typed x + h.

You typed mismatched grouping symbols on the lefthand side of your "equation" and no grouping symbols on the righthand side.

And, I'm thinking that your "equation" is not even supposed to be an equation.

Also, the symbols X and x are not the same; they are not interchangable.

Overall, I have to guess what you mean.

:idea: Nobody can see where your mistakes are located unless you show us your work.


\(\displaystyle \frac{\sqrt{x} \;-\; \sqrt{x + h}}{h \ \sqrt{x} \ \sqrt{x + h}} \cdot \frac{\sqrt{x} \;+\; \sqrt{x + h}}{\sqrt{x} \;+\; \sqrt{x + h}} \;=\; \frac{1}{h \ \sqrt{x + h}} \;-\; \frac{1}{h \ \sqrt{x}}\)

 

[Zerrotolerance]

That is what I meant. Sorry, it's my first time here, otherwise I would have shown it better if I knew how to get the square root symbol to print out. It wasn't supposed to be an equation, I was trying to explain it in words in case I typed the other part out wrong like you pointed out. Where do you find things like square roots, so I can show my problems and work like you did. I didn't want to type out all the work because I figured no one would read 5 lines like my:

((sqr(x) - sqr(x+h))/(h(sqr(x)(sqr(x+h)))

I ended up getting the answer right(the same one you gave me) by using the propFrac App on my calculator, but I wanted to do it by hand to understand it. I found out I was multiplying the denominator by the conjugate wrong. Looks like I need to brush up on square roots and how they function.

 

[mmm4444bot]

I figured no one would read 5 lines like my:

((sqr(x) - sqr(x+h))/(h(sqr(x)(sqr(x+h)))

I would.

It is much easier (for me) to decipher intent from work shown versus trying to understand mistakes in work that I cannot see.

I mean, the more information there is in front of me, the better I can recognize mistakes as typographical errors versus errors in algebra or logic.

Cheers

PS: Maybe you find the following notations easier to read.

(sqrt[x] - sqrt[x+h]) / (h sqrt[x] sqrt[x + h])

OR

[sqrt(x) - sqrt(x + h)] / [h sqrt(x) sqrt(x + h)]