Welch Knight
10/16/2023 · Elementary School
1. Given the function \( y=4 \sin (2 \theta-1)+2 \), find: a. One local maximum. b. One local minimum. c. One \( x \)-intercept on the negative \( x \)-axis. d. One \( x \)-intercept on the positive \( x \)-axis.
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a. One local maximum: \( \left( \frac{\pi + 2}{4}, 6 \right) \)
b. One local minimum: \( \left( \frac{3\pi + 2}{4}, -2 \right) \)
c. One \( x \)-intercept on the negative \( x \)-axis: \( \left( \frac{1 - 5\pi}{12}, 0 \right) \)
d. One \( x \)-intercept on the positive \( x \)-axis: \( \left( \frac{7\pi + 6}{12}, 0 \right) \)
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