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If the function f(x) =axe^(bx^(2)) has m...

If the function f(x) =`axe^(bx^(2))` has maximum value at x=2 such that f(2) =1 , then find the values of a and b

Text Solution

Verified by Experts

The correct Answer is:
`a=sqrt(e )/(2),b=1/8`
f(x) =`axe^(be^(2))`
According to the question
f(x)=1 and f(2)=0
`therefore 2ae^(4b)=1`
Also `f(x) =a[xe^(bx^(2))].2bx+e^(bx^(2)) =ae^(bd)[2bx^(2)+1]`
`f(2)=ae^(4b)(8b+1)=0`
`therefore f(x)=(sqrt(e ))/(2)^(1/8)x^(2)[(1/4x^(2)+1)]`

clearly,x=2 is point of maxima.
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