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Find the local maxima and local minima o...

Find the local maxima and local minima of the functions:
(i) `f(x) = sin 2x, " when " 0 lt x lt pi`
(ii) `f(x) = (sin 2x -x), " when " - (pi)/(2) le x le (pi)/(2)`

Text Solution

AI Generated Solution

To find the local maxima and minima of the given functions, we will follow these steps: 1. **Find the first derivative of the function.** 2. **Set the first derivative equal to zero to find critical points.** 3. **Determine the second derivative.** 4. **Evaluate the second derivative at the critical points to classify them as local maxima or minima.** 5. **Check if the critical points lie within the given interval.** ...
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