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Question: If the function f(x) = x(x + 4).\(e ^ { - \frac { x } { 2 } }\) has it's local maxima at x = a then...

If the function f(x) = x(x + 4).e−x2e ^ { - \frac { x } { 2 } } has it's local maxima at

x = a then

A

a = 4

B

a = 1 −3\sqrt{3}

C

a = -1+ 3\sqrt{3}

D

) a = -4

Answer

a = 4

Explanation

Solution

f '(x) = −12e−x2(x2−16)- \frac { 1 } { 2 } e ^ { - \frac { x } { 2 } } \left( x ^ { 2 } - 16 \right)

Clearly x = 4 is the point of local maxima.