How to evaluate f'' at a specific point?
05-22-2015, 05:49 PM
Post: #1
 lrdheat Senior Member Posts: 860 Joined: Feb 2014
How to evaluate f'' at a specific point?
Dumb question...how in home or CAS do I enter f''(3 root (x-2)) where x=some number of interest?
05-22-2015, 06:46 PM
Post: #2
 DrD Senior Member Posts: 1,133 Joined: Feb 2014
RE: How to evaluate f'' at a specific point?
Did you try:

(x-2)^(1/3)''

or:

∂((x-2)^(1/3),x)'
05-22-2015, 07:20 PM
Post: #3
 lrdheat Senior Member Posts: 860 Joined: Feb 2014
RE: How to evaluate f'' at a specific point?
In trying to get the second derivative at a specified point, I'm having difficulty in accessing the proper syntax. The template gives me d/dx. I can then get, say, ((d 3 root x-2 / dx)/dx))|x=1.99.
This returns 0 instead of 478+. What am I doing wrong?
05-22-2015, 08:42 PM (This post was last modified: 05-22-2015 08:53 PM by Helge Gabert.)
Post: #4
 Helge Gabert Senior Member Posts: 467 Joined: Dec 2013
RE: How to evaluate f'' at a specific point?
I would just do

diff(diff(3ROOT(x-2),x),x) and then
Ans|x=1.99 (Ans actually has to be copied explicitly from the command line above)

returns 478.76 . . . for me.

Or do you have to do it with the d/dx template?

[You can also define f(x):=3Root(x-2), and then simply type f''(1.99) also returns 478.76 . . .]
05-22-2015, 09:03 PM
Post: #5
 lrdheat Senior Member Posts: 860 Joined: Feb 2014
RE: How to evaluate f'' at a specific point?
That works (thanks!). Seems like there should be a more direct way to do this.
05-22-2015, 09:50 PM (This post was last modified: 05-22-2015 09:59 PM by toshk.)
Post: #6
 toshk Member Posts: 195 Joined: Feb 2015
RE: How to evaluate f'' at a specific point?
(∂(∂((x-2)^(1/3),x),x)|(x )= 1.99)
Credit: Eddie's Math and Calculator Blog series, by Edward Shore
3.24.

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05-23-2015, 05:49 AM
Post: #7
 parisse Senior Member Posts: 1,323 Joined: Dec 2013
RE: How to evaluate f'' at a specific point?
More natural syntax:
f(x):=(2-x)^(1/3);
f''(1.99)
For a large number of derivatives, for example 5, run diff(f(x),x,5)(x=1.99)
05-23-2015, 04:11 PM
Post: #8
 lrdheat Senior Member Posts: 860 Joined: Feb 2014
RE: How to evaluate f'' at a specific point?
Thanks...this is what I hoped for! And when using the n root entry, negative results are produced for this equation directly as opposed to a complex number result!
05-23-2015, 04:19 PM
Post: #9
 lrdheat Senior Member Posts: 860 Joined: Feb 2014
RE: How to evaluate f'' at a specific point?
Can this syntax be used in the function graphing app...the diff(f(x),x,2) form? What is the proper syntax for this?
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