This problem uses a TI-89 calculator)
Find the largest and smallest values of the following function on their given intervals:
y=(cos x)^x
[-1.5, 4.75]
This is what I put in the calculator (home screen):
fMin((cos(x))^x,x I -1.5 < x < 4.75
(I = "with" symbol, < is less than or equal to)
I keep getting the error message that says domain error. Help please?
Thanks!
is the domain of x in radians, degrees, or what? Is that what your calculator is set at?
x is in degrees, yes.
To find the largest and smallest values of the function y = (cos x)^x on the given interval [-1.5, 4.75] using a TI-89 calculator, you can follow these steps:
1. Enter the function in the calculator:
a. Press the HOME button to go to the home screen.
b. Type (cos(x))^x using the cos function and the exponent (^) symbol.
2. Use the fMin and fMax functions to find the smallest and largest values of the function respectively:
a. Type fMin((cos(x))^x, x, -1.5, 4.75) to find the smallest value.
b. Type fMax((cos(x))^x, x, -1.5, 4.75) to find the largest value.
However, it seems that you are encountering a domain error with the current setup. In this case, it is possible that the function has undefined values or your calculator settings need adjustment.
Here are a few things you can try to resolve the issue:
1. Adjust calculator settings:
a. Go to MODE.
b. Make sure the angle measurement is set to radians since the function involves trigonometric functions. If it is set to degrees, change it to radians.
2. Modify the interval:
a. The domain of y = (cos x)^x is limited due to the nature of the function. Try narrowing down the interval to a smaller range or choose a different interval where the function will have valid values.
For instance, you could try using an interval like [-1, 1] or [-1, 0.5] to see if that resolves the issue.
By following these steps and making the necessary adjustments, you should be able to find the largest and smallest values of the function on the provided interval using your TI-89 calculator.