39gii bizarre graph extremum

05172014, 07:49 PM
Post: #1




39gii bizarre graph extremum
When plotting x^(2/3) * (6x)^(1/3), the function plots fine (I chose to plot from .5 to 6.5, and then used auto scale). When I asked for extremum, it comes up with a point well to the right of the extremum! The actual extremum is (4,~3.17+). The 39gii plot places it at (~4.98,~2.94)!
When I go to solve and take d/dx of the function to be zero, it correctly comes up with 3.9999999999 (4). Area under curve between roots (which it finds correctly) impossible. 

05192014, 02:31 AM
Post: #2




RE: 39gii bizarre graph extremum
More notes...the above function, when entered as (3 root x)^2 * 3 root (6x) is not so bizarre in plot...extremum is correctly found at (4,3.17+).
The pattern that I find on the HP 39gii is that (n root y)^z works better than fractional powers. In plot, if f'(x) is discontinuous within or at the endpoints of an area of interest (in this case, at 0), signed area will take a long time, and will come up with a nonsensical answer. If one takes the area from at least .001 away from the discontinuity, an accurate answer will be found (for your new interval which in most cases, will closely approximate the real answer). In home, the integration is less forgiving. The above integral is successfully calculated (after a minute or two) with endpoints of 5 to .5. After several minutes integrating from5 to .1, it gave me the ER: invalid input. Changing from standard to fix 2 did nothing to help the situation. Recognizing these issues, I can more confidently use the calculator. I know now what type of problems will present difficulties. In plot mode, analysis of the function including area under or beteeen curves is exceptionally quick and accurate (not tied down to how close to a number of interest a pixel happens to be). Much faster than home mode calculus functions. Easy to define graph domain, range...autoscale handy as well. Zoom works well. Amazingly, d/dx can be entered into solve to find a slope of interest. Number table is also quite handy. Copy and paste quite handy, and variable management for calculations is excellent. Like that it uses AAA batteries that will last a year of a fair amount of daily use. Still have much more to explore on this calculator and the Prime. Mainly working them as graphing calculating tools, not heading in the direction of taking advantage of their programing potential... Look forward to whenever a new firmware emerges. Prime, of course, can handle the above plot issues competently, and it is a treat to use the touch screen. While the HP 39gii is shirt pocketable, the Prime easily slides in my shirt pocket (may look for something to slide it inside of so that it will not easily spill out of a shirt pocket should I lean over to pick something up...). Look forward to whenever the new firmare for the Prime emerges as well. 

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