Also with calculator, graph f(x), and determine all the possible maxima/minima coordinates to within two decimal points.
f(x)=x^3+2x^2-x-2/x^2+x-6
i did this and got my answers but i doubt they are right, can anyone get the answers if you have a TI-83-84 please? thank you.
Could you post your answers if you need a confirmation?
Also, calculate f'(x) and substitute the x-coordinate of the maximum/minimum to see if f'(x)=0. This will be another way to confirm your answer.
my answer is :
maxima: x= -1.56
minima:x=-1.29, x=-1.25
f'(x)=3*x^2+4*x+4/x^3
f'(-1.56)=0.0072
f'(-1.559)=-0.00021
Therefore x=-1.56(approx.) is a maximum or minimum.
f"(x)=6*x-12/x^4+4
f"(-1.56)=-7.386 >0
Therefore x=-1.56 is a maximum.
f'(-1.29)=-2.03 ≠ 0
f'(-1.25)=-2.3605 ≠ 0
Therefore x=-1.29 and x=-1.25 are not maxima nor minima.
Check your graph without forgetting that the function is undefined at x=0.
oh thank you so much, so x=-1.56 is a maxima, and we don't have a minima?
To graph the function f(x) and determine the possible maxima and minima coordinates using a TI-83 or TI-84 calculator, follow these steps:
1. Turn on your calculator and press the "Y=" button to enter the function editor.
2. Clear any existing functions by pressing the "Clear" button.
3. Enter the function f(x) as follows:
- Press the "X^2" button on the calculator keypad.
- Press the "+/-" button to enter a negative sign.
- Press the "X^3" button.
- Press the "+" button.
- Press the "2" button.
- Press the "X^2" button.
- Press the "-" button.
- Press the "X" button.
- Press the "-" button.
- Press the "2" button.
- Press the "/" button.
- Press the "X^2" button.
- Press the "+" button.
- Press the "X" button.
- Press the "-" button.
- Press the "6" button.
4. After entering the function, press the "Graph" button to plot the graph of f(x).
To determine the possible maxima and minima coordinates on the graph, you can use the calculator's "Minimum" and "Maximum" functions. Follow these steps:
1. After graphing the function, press the "2nd" button, followed by the "Calc" button.
2. Select option 3, "Minimum/Maximum."
3. The calculator will prompt you to specify a left bound (minimum x-value).
- Move the cursor to the left of the point where you suspect a minimum or maximum may exist on the graph.
- Press the "Enter" button to set the left bound.
4. The calculator will then prompt you to specify a right bound (maximum x-value).
- Move the cursor to the right of the point where you suspect a minimum or maximum may exist.
- Press the "Enter" button to set the right bound.
5. The calculator will display the coordinates of the minimum or maximum point, including the x-value and the y-value.
Repeat steps 3-5 for any other points where you suspect a minimum or maximum may exist.
By following these steps, you can use a TI-83 or TI-84 calculator to graph the function f(x) and determine the possible maxima and minima coordinates with two decimal points accuracy.