diff --git a/education/math/MATH1210 (calc 1)/Max and Min.md b/education/math/MATH1210 (calc 1)/Max and Min.md index dd94c2a..01b79c7 100644 --- a/education/math/MATH1210 (calc 1)/Max and Min.md +++ b/education/math/MATH1210 (calc 1)/Max and Min.md @@ -40,5 +40,6 @@ If $f$ is a continuous function in a closed interval $[a, b]$, then $f$ achieves 5. In the interval $[0, \pi]$, $\sin(x)$ has a value of $\dfrac{1}{2}$ in two places: $x = \dfrac{\pi}{6}$ and $x = \dfrac{5\pi}{6}$. These are both critical numbers because they are points where $\dfrac{d}{dx}$ is zero. 6. Now we plug these values into the original function: 7. $h(0) = 0 + 2\cos 0 = 2$ - 8. $h(\pi) = \pi + 2\cos(\pi) = \pi - 2$ - 9. $h(\dfrac{pi}{6}) = \dfrac{\pi}{6} + 2\cos(\dfrac{pi}$ + 8. $h(\pi) = \pi + 2\cos(\pi) = \pi - 2 \approx 1.14159$ + 9. $h(\dfrac{\pi}{6}) = \dfrac{\pi}{6} + 2\cos(\dfrac{\pi}{6}) = \dfrac{\pi}{6} + 2(\dfrac{\sqrt{3}}{2} = \dfrac{\pi}{6} + \sqrt{3} \approx 2.2556$ + 10. $h(\dfrac{5\pi}{6}) = \dfrac{5\pi}{6} + 2\cos(\dfrac{5\pi}{6}) = \dfrac{5\pi}{6} - \sqrt{3} \approx 0.88594$