that is an input for which height-sign comes from h0 and slope-sign comes from h1 and concavity-sign comes from h2.
As opposed to critical bounded inputs which are inputs for which height-sign comes from h1 or higher, or slope-sign comes from h2 or higher, or concavity-sign comes from h3 or higher.
At this time, only the first three buttons, namely the local graph button, the declare button and the execute button, work.
At the bottom of this page is the---very clunky---animation of the top of the page. I hope that my next attempt will give better results.
Clicking on a band opens it and closes the previous one. The first one is already open.
Finally, give your browser a bit of time to compile the math. You will know when it's done because the math will then look really good.
GIVEN: The function CUBIC specified by the global input-output rule
xCUBIC→CUBIC(x)=−4x3−10x2+7x−15
WANTED: The
jQuery UI Dialog functionality
of CUBIC for inputs
near +2
.
PLANNING AHEAD: What is going to be your overall line of attack to get what is wanted?
Get the global graph of CUBIC and highlight the local graph near +2 ?
Get the local graph near ∞ of the power function
xa→a(x)=−4x3
?
Get the local input-output rule near +2 from the global input-output rule of CUBIC?
Get the global graph of the power function
xa→a(x)=−4x3
?
DO:
In the given global input-output rule,
jQuery UI Dialog functionality
the input to be
near +2
:
CUBIC(+2+h)
using the
for
x|x←+2+hCUBIC→CUBIC(x)|x←+2+h=−4x3−10x2+7x−15|x←+2+h +2+hCUBIC→CUBIC(+2+h)=−4(+2+h)3−10(+2+h)2+7(+2+h)−15(x0+h)3 and for (x0+h)2:
Since the exponent is 0 and the coefficient is negative, the local graph of K near 0 is:
the local graph of
xK→K(x)=−1x0
from 0 to +2.
the power function
xL→L(x)=−1x+1.
Since the exponent is +1 and the coefficient is negative, the local graph of L near 0 is:
the local graph of
xL→L(x)=−1x+1
from 0 to +2.
the local graph of L to the local graph of K
the power function
xQ→Q(x)=−1x+2.
Since the exponent is positive even and the coefficient is negative, the local graph of Q near 0 is:
the local graph of
xQ→Q(x)=−1x+2
from 0 to +2,
the local graph of Q to the local graph of K+L
Local Graph near a given bounded input
The local graph of a given function f near a given bounded input x0 is the graph of the approximate input-output rule of f for inputs nearx0 namely:
x0+hf→f(x0+h)=[A0]h0+[A1]h1+[A2]h2+[...]
To declare a specific input
To declare an input is to say which specific input is to be used. It is coded as follows
|x←specific input
To execute a declaration
To execute a declaration is actually to replacex by the given input.
To declare a specific input
To declare an input is to say which specific input is to be used. It is coded as follows
|x←specific input
To execute a declaration
To execute a declaration is actually to replacex by the given input.
