Consider the function $f ( x ) = e ^ { - ( x - 6 ) ^ { 2 } / 5 }$ .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 = 6,f (6)= 1
B) $x = \frac { 3 } { 5 }$ , $f \left( \frac { 3 } { 5 } \right)$ $\approx$ 0.00
C)There is no maximum.
D) $x = \frac { 6 } { 5 }$ , $f \left( \frac { 6 } { 5 } \right)$ $\approx$ 0.01

Question

Quizplus · Accepted Answer

The function $f(x) = e^{-\frac{(x-6)^2}{5}}$ is a Gaussian function centered at $x = 6$. The maximum value of this function occurs at the center of the Gaussian, which is $x = 6$, because the exponent reaches its maximum value (0) at this point, making $f(6) = e^0 = 1$.

Consider the Function f(x)=e−(x−6)2/5f ( x ) = e ^ { - ( x - 6 ) ^ { 2 } / 5 }f(x)=e−(x−6)2/5

Consider the Function $f ( x ) = e ^ { - ( x - 6 ) ^ { 2 } / 5 }$