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If the function f(x)=ax e^(-bx) has a lo...

If the function `f(x)=ax e^(-bx)` has a local maximum at the point (2,10), then

A

a = 5e

B

a = 5

C

b = 1

D

b = 1/2

Text Solution

Verified by Experts

The correct Answer is:
A, D
`f(x)=ax e^(-bx)` hs a local maximum at the point (2, 10)
`therefore" "f(2)=10,2ae^(-2b)=10`
`rArr" "ae^(-2b)=5" (i)"`
`f'(x)=a[e^(-bx)-bx e^(-bx)]`
`f'(2)=0`
`rArr" "a(e^(-2b)-2b^(-2b))=0`
`rArr" "ae^(-2b)(1-2b)=0`
`rArr" "b=1//2`
From (i) if b = 1/2, then
a = 5e or a = 0 (not possible)
`therefore a=5e and b=1//2`
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