Răspuns:
D
Explicație pas cu pas:
[tex]E^{\prime} (x) = \Big( \cos^{2} x - 4 \sin x \Big)^{\prime} = - \sin(2x) - 4 \cos(x) = \\ = - 2 \sin(x) \cos(x) - 4 \cos(x) = - 2\cos(x)(\sin(x) + 2)[/tex]
[tex]E^{\prime} (x) = 0 \implies - 2\cos(x)(\sin(x) + 2) = 0 \\ [/tex]
[tex]\sin(x) + 2 = 0 \iff \sin(x) = - 2 \\ fara \ \ \ solutii[/tex]
[tex] \cos(x) = 0 \implies \\ x = \frac{\pi}{2} + 2k\pi; \ \ x = \frac{3\pi}{2} + 2k\pi[/tex]
minim:
[tex]E\Big( \frac{\pi}{2} \Big) = - 4[/tex]
maxim:
[tex]E\Big( \frac{3\pi}{2} \Big) = 4[/tex]
