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 an exponential function occurs at its peak, which is at $x = 6$ for this function. At $x = 6$, the exponent becomes 0, making $f(6) = e^0 = 1$. Therefore, the function attains its maximum value at $x = 6$, and the maximum value is 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 $f ( x ) = e ^ { - ( x - 6 ) ^ { 2 } / 5 }$