Finding Roots of Derivatives on Casios

[Matt Agajanian]

Hi all. I put in the expression d/dx(3x^3-10x^2+15) x=x
Next, I opened SOLVE and put in an initial guess. After I press =, I get Syntax Error.

So, I entered the same thing, except I set x=x. Nope. Syntax Error again.

So, I tried writing it as 0=d/dx(3x^3-10x^2+15) and pressed SOLVE. Put in an initial guess. Nope. Syntax error.

If there’s a way to find roots of derivatives on the 991, 115, and ClassWiz models, how do I do that?

Thanks

[klesl]

For 115/991: excerpt from UG
Important!
If an equation contains input functions that include an open parenthesis (such as sin and log), do not omit the closing parenthesis.
The following functions are not allowed inside of an equation: ∫, d/dx, Σ, Pol, Rec.
https://support.casio.com/global/en/calc...SOLVE.html

For 991EX (ClassWiz)
d/dx(3x^3-10x^2+15) /x=A=0; solve for A, the 2nd equation sign next to the 0 is red on the keyboard (alpha+calc)
press shift+calc (solve)
scroll down to see A (not X) and enter value
press enter to get the root x=2.2222222222 or 20/9 and x=0

[Matt Agajanian]

(11-19-2022 11:26 AM)klesl Wrote:  For 115/991: excerpt from UG
Important!
If an equation contains input functions that include an open parenthesis (such as sin and log), do not omit the closing parenthesis.
The following functions are not allowed inside of an equation: ∫, d/dx, Σ, Pol, Rec.
https://support.casio.com/global/en/calc...SOLVE.html

For 991EX (ClassWiz)
d/dx(3x^3-10x^2+15) /x=A=0; solve for A, the 2nd equation sign next to the 0 is red on the keyboard (alpha+calc)
press shift+calc (solve)
scroll down to see A (not X) and enter value
press enter to get the root x=2.2222222222 or 20/9 and x=0

Thanks! That works.

[Matt Agajanian]

Okay. Now I’ve got a first root.

How do I store this first root and repeat the process with a different estimate/guess and store that solution?

I tried a STO A from the L-R screen but it gets all messed up and I cannot see my equation in the history list. So, either I'm missing a step or my procedure is wonky.

Please advise.

Thanks.

[klesl]

Well, you don't need to store the root because the root is stored automatically to memory A.
To find another root, just use solver again:
When you see the root and L-R on the screen, press the right arrow and change initial value from A to B and start solver.
Now you have 2 roots stored in A and B

[Matt Agajanian]

(11-20-2022 05:35 PM)klesl Wrote:  Well, you don't need to store the root because the root is stored automatically to memory A.
To find another root, just use solver again:
When you see the root and L-R on the screen, press the right arrow and change initial value from A to B and start solver.
Now you have 2 roots stored in A and B

Thanks! I definitely know what you mean.

[Matt Agajanian]

On another tangent (pun intended).

Is there such a thing as finding roots of derivatives by deflation?

For example:

With a as the first root of f’(x)
is it legitimate to apply the deflation formula of f’(x)/(x-a) to find the second zero, thus the second extremum? Or is there another formula instead?