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

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

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

extreme points

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

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 7,

Decreasing

: 7 < x < \infty

Plug

x = 7

into

\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}}})

(\frac{9}{2}, \frac{3}{8}), (- \frac{11}{2}, \frac{5}{8})

0.2 x^{2} + 3 x - 20

(1, - 1), (4, - 3)

f (x) = \frac{x}{2} - 3

f (y) = 4 y

What is the extreme f(x)= 1/(sqrt(2pi))e^{(-(x-7)^2)/2} ?
The extreme f(x)= 1/(sqrt(2pi))e^{(-(x-7)^2)/2} is Maximum(7, 1/(2^{1/2)pi^{1/2}})