One Problem For Another...
All right. At last I know where I went wrong: a little sign change poked its ugly head in there at the last minute, and where it should have read, A=2x^3+x, it read A=2x^3-x. So that helps somewhat. However, that graph looks like this:
As you can see, I am now stuck with the opposite problem; You could give me an x, say, -.25, and my new better function will give you a positive number! I'll let the $20 stand...
As you can see, I am now stuck with the opposite problem; You could give me an x, say, -.25, and my new better function will give you a positive number! I'll let the $20 stand...
posted by P. Robinson at 7:05 PM
1 Comments:
Hey Paul,
This occurred to me just as I was falling asleep.
I did find where you went wrong. I actually didn't see your solution until I worked it out myself and discovered that we arrive at it pretty differently. I am too lazy to type in all of the math but I will show you some.
I found the tangent lines to the square function to be as follows as the value of z changes.
f(z)=2(z)x-z^2
This will give you the slope formula for every tangent line for every value of z
The reciprocal is:
f(a)=-1/(2a)x+a^2+1/2
This is what you arrived at when taking the derivative. Set f(a) to 0 because you want the x intercept and solve. You get the same as you found.
x=2a^3+a
The a will always place the point as far as the point on the x^2 function from the origin. the 2 coefficient is from the exponent (shape) of the original function. The cubic function allows it to work on both sides of the origin. When you checked -1/4 I think you made an error because if you are using a cubic function and adding that number to it, the sign should never change.
2(-1/4)^3+(-1/4)
2(-1/16)-(1/4)
-1/8-(1/4)
-3/8
As you see, this works out just fine and you have solved it without realizing it. The cubic graph that you have at the bottom is not correct. The cubic function will pass through the origin as is your value is 0. 2(0^3) +0=0. That is where you may see some discrepancy.
Best wishes.
Jason Alfred
However, when you checked your math
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