determine the minima, maxima, and inflection points?

Question

f(x)=2xcubed-3xsquared+x-4

Answer 1

You will need a scientific graphing calculator for this one.
You go to "y=" and type in 2xcubed - 3xsquared + x - 4 and hit "graph". (NOTE: To type in exponents use the carrot button. Ex: 2x (carrot) 3 is = to 2xcubed)

Then hit "2nd" "trace". Scroll down to "minimum" or "maximum", whichever you want to do first. Then once you have chosen one hit enter and it will take you back to your graph.

I chose minimum for the example. A cursor will appear on the graph. It will say "Left Bound?" at the bottom. At this point you will move the cursor to the left of the lowest point on your graph. Hit "enter". Now you will see "Right Bound?". With the arrows, move it to the right of the same, lowest point.

You will now see "Guess?" at the bottom of your screen. You will hit "enter" again. What this does is it picks the lowest point on the graph inbetween the two you picked, which were the left and right bound points. The answer is x=.78867628 y= -4.096225

Now just repeat the steps to solve the maximum. The only difference is that now you will choose the "left" and "right bound" points of your highest point on the graph.

I used a Texas Instruments TI-83 Plus calculator but the instructions should be similar for any.

Hope this helps. If you need more help just ask! Good luck!

Answer 2

First, use a carat to indicate powers, like 2x^3.

Maximum and minima are found from inspection of the 1st derivitive of the function, which is
6x^2 - 6x +1
when set to zero. This means finding the roots of the quadratic above and checking whether you are at a minimum or maximum.

Inflection is found from the second derivitive, which is 12x -6
When set to zero, this yield an inflection at x=1/2.