Consider the function $f ( x ) = e ^ { - ( x - 8 ) ^ { 2 } / 7 }$ . For what value of x does this function attain its maximum value, and what is the maximum function value? Round maximum function value to two decimal places, if necessary.
A) $x = \frac { 8 } { 7 } , f \left( \frac { 8 } { 7 } \right) \approx 0.00$
B) x = 8, f (8) = 1
C) $x = \frac { 4 } { 7 } , f \left( \frac { 4 } { 7 } \right) \approx 0.00$
D) There is no maximum.

Question

Quizplus · Accepted Answer

The function $f(x) = e^{-\frac{(x-8)^2}{7}}$ is a Gaussian function centered at $x = 8$. The maximum value occurs at the center of the Gaussian, where $x - 8 = 0$, thus at $x = 8$. At this point, the function value is $f(8) = e^0 = 1$, making it the maximum value of the function.

Consider the Function f(x)=e−(x−8)2/7f ( x ) = e ^ { - ( x - 8 ) ^ { 2 } / 7 }f(x)=e−(x−8)2/7

Consider the Function $f ( x ) = e ^ { - ( x - 8 ) ^ { 2 } / 7 }$