analyze the function for domain, range, continuity, increasing or decreasing behavior, symmetry…

analyze the function for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. f(x)=sin⁻¹x the function is bounded. identify any local maxima. select the correct choice and, if necessary, fill in the answer box to complete your choice. a. there is a maximum at x = 1. (simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression. use a comma to separate answers as needed.) b. there are no local maxima. identify any local minima. select the correct choice and, if necessary, fill in the answer box to complete your choice. a. there is a minimum at x = . (simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression. use a comma to separate answers as needed.) b. there are no local minima.
Answer
Answer:
- A. There is a maximum at (x = 1)
- B. There are no local minima
Explanation:
Step1: Recall domain and properties of (y = \sin^{-1}x)
The domain of (y=\sin^{-1}x) is ([- 1,1]) and it is an increasing - function on its domain.
Step2: Determine local maxima
Since (y = \sin^{-1}x) is increasing on ([-1,1]), the maximum value occurs at (x = 1) and (\sin^{-1}(1)=\frac{\pi}{2}).
Step3: Determine local minima
As the function is increasing on ([-1,1]), there are no local minima.