I found the equation using the excel linest function which came out to be 10.35x
ID: 927239 • Letter: I
Question
I found the equation using the excel linest function which came out to be
10.35x^5 + 85.92x^4 - 246.7x^3 + 280.98x^2 - 130.56x + 89.2
Also,
I found the second derivative to be
207x^3 + 1030.92x^2 - 1480.2x+561.96
Where i got stuck is calculating the inflection point. Visually i can tell its supposed to 1.85ish. But, I cant get close to that value.
A chemical reactor is thermally stratified as in the following table: As depicted in the figure below, the reactor can be idealized as two zones separated by a strong gradient or thermocline. The depth of this thermocline can be defined as the inflection point of the temperature .vs. depth curve - that is. the point at which: d^2T/dz^2 = 0 Use the method of least squares (and Excel's LINEST function) to fit a polynomial curve to this set of data and determine the depth of die thermocline. The choice of the order of the polynomial is yours.Explanation / Answer
I plotted the graph in excel and my equation comes out to be
y=-10.349x^5 + 85.92*x^4 -246.71x^3+280.98*x^2 -130.56*x+89.209
Now at the inflection point, the second derivative will be 0.or,
-10.349*4*5*x^3 + 85.92*4*3*x^2 - 246.71*3*2*x + 280.98*2=0
Solving for x, we get
x=1.66
you can use this app to find the inflection point : http://www.wolframalpha.com/widget/widgetPopup.jsp?p=v&id=c76b1b218228841bbae6a672d1fc5674&title=Inflection%20Point%20Calculator&theme=blue&i0=-10.349x%5E5%20%2B%2085.92*x%5E4%20-246.71x%5E3%2B280.98*x%5E2%20-130.56*x%2B89.209&podSelect=&includepodid=Input&includepodid=Result&includepodid=Plot&podstate=Result__Show%20details&showAssumptions=1&showWarnings=1
Note: The app is the property of Wolfram alpha.
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