Question

The function exp(−2(𝑥-1)²) attains a maximum at 𝑥= _______. (rounded off to the nearest integer)

Answer 1

Correct Answer: 1

The given function is \( f(x) = \exp(-2(x - 1)^2) \).

To find the maximum, we first compute the derivative of the function:

\( f'(x) = \frac{d}{dx} \exp(-2(x-1)^2) = \exp(-2(x-1)^2) \cdot (-4(x-1)) \)

Setting \(f'(x) = 0\) to find the critical points:

\( \exp(-2(x -1)^2) \cdot (-4(x -1)) = 0 \)

Since \( \exp(-2(x - 1)^2) \neq 0 \), we have:

\( -4(x - 1) = 0 \Rightarrow x=1 \)

Thus, the function attains a maximum at \( x = 1 \).