Mamaha olana matematika

Dingana amin'ny dingana

1. f(x) = \sin{\left(x \right)}

   Critical points are where f′(x) = 0 or is undefined.

2. f'(x) = \cos{\left(x \right)}

   Differentiate.

3. x = \frac{\pi}{2}, x = \frac{3 \pi}{2}

   Solve f′(x) = 0.

4. f''(x) = - \sin{\left(x \right)}

   Second-derivative test: f″ < 0 → maximum, f″ > 0 → minimum.

5. f''(\frac{\pi}{2}) = -1 \Rightarrow (\frac{\pi}{2}, 1) \text{ is a local maximum}

6. f''(\frac{3 \pi}{2}) = 1 \Rightarrow (\frac{3 \pi}{2}, -1) \text{ is a local minimum}