Consider the function f(x)= begincasesx(x-1) e2 x, text if x ≤ 0 x(1-x) e-2 x, text if x0 endcases. Then f ( x ) attains its greatest value at

Question

Consider the function f(x)= begincasesx(x-1) e2 x, text if x ≤ 0 x(1-x) e-2 x, text if x>0 endcases. Then f ( x ) attains its greatest value at (A) 1-(1/√2) (B) 1+(1/√2) (C) (-1/√2) (D) (1/√2)

Tardigrade Admin · Accepted Answer

Global maximum at x=(-1/√2) ; ∵ f(-(1/√2))> f (1-(1/√2))

Q. Consider the function $f (x) = {x (x - 1) e^{2 x}, x (1 - x) e^{- 2 x}, if x \leq 0 if x > 0$ .
Then $f (x)$ attains its greatest value at

$1 - \frac{1}{2}$

$1 + \frac{1}{2}$

$\frac{- 1}{2}$

$\frac{1}{2}$

Global maximum at $x = \frac{- 1}{2}; ∵ f (- \frac{1}{2}) > f (1 - \frac{1}{2})$

Q. Consider the function f(x)={x(x−1)e2x,x(1−x)e−2x,​ if x≤0 if x>0​. Then f(x) attains its greatest value at

1−2​1​

1+2​1​

2​−1​

2​1​