Question

Sa se determine cea mai mica si cea mai mare valoare a functiilor:
a) f(x)=2^(cos x)
b) f: [$\frac{ \pi }{4} , \pi$] →R, f(x)= sin x

Answer 1

   
[tex]\displaystyle \\ a) \\ f(x) = 2^{(\cos x)}\\ f(x) = minim ~ pentru ~ x = \pi + 2k\pi \\ \\ f(\pi) = 2^{(\cos \pi)} = 2^{(-1)} = \boxed{\frac{1}{2} } \\ \\ f(x) = maxim ~ pentru ~ x = 0 + 2k\pi \\ \\ f(0) = 2^{(\cos 0)} = 2^{1} = \boxed{2} [/tex]



[tex]\displaystyle \\ b) \\ f:\Big[ \frac{\pi}{4},~\pi \Big] \rightarrow R , ~~f(x) = \sin x \\ \\ f(x) = minim ~pentru~x= \pi \\ f(\pi) = \sin \pi = \boxed{0} ~~~~unde ~\pi \in \Big[ \frac{\pi}{4},~\pi \Big] \\ \\ f(x) = maxim ~pentru~x= \frac{\pi}{2} \\ \\ f(\frac{\pi}{2} ) = \sin \frac{\pi}{2} = \boxed{1} ~~~~unde ~\frac{\pi}{2} \in \Big[ \frac{\pi}{4},~\pi \Big] [/tex]