extreme f(x)= 1/(sqrt(2pi))e^{(-(x-7)^2)/2}

Lösung

extrempunkte

f (x) = \frac{1}{2 π} e^{\frac{- ( x - 7 ) ^{2}}{2}}

Maximum (7, \frac{1}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}}})

Schritte zur Lösung

f^{'} (x) = \frac{1}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}}} e^{- \frac{( x - 7 ) ^{2}}{2}} (- x + 7)

Intervalle finden:

Ansteigend

: - \infty < x < 7,

Absteigend

: 7 < x < \infty

Stecke

x = 7

\frac{1}{2 π} e^{\frac{- ( x - 7 ) ^{2}}{2}} : \frac{1}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}}}

Maximum (7, \frac{1}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}}})

mi d p o in t (\frac{9}{2}, \frac{3}{8}), (- \frac{11}{2}, \frac{5}{8})

a sy m pt o t es 0.2 x^{2} + 3 x - 20

d i s t an ce (1, - 1), (4, - 3)

in t erce pt s f (x) = \frac{x}{2} - 3

f (y) = 4 y