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In a question a student was given to find the derivative of the product of two functions `fa n dgdot` The student y misstate thought `(fg)^'=f'g'` for his question `f(x)=x^3` and he got the correct answer. Given that `g(4)=1.` Then which of the following is false? `g(5)=1/8` b. `f^(prime)(x)<0` c.`f(0)<0` d. none of these

A

`g(5)=(1)/(8)`

B

`f'(x)lt0`

C

`f(0)lt0`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`(fg)'=f'g'`
`therefore" "fg'+f'g=f'g'`
`therefore: "xg'+3g=3g'`
`therefore" "(x-3)g'+3g=0`
`therefore" "(x-3)^(3)g'+3(x-3)^(2)g=0`
`therefore" "(g(x-3)^(3))'=0`
`therefore" "(x-3)^(3)g(x)=c`
`therefore" "g(x)=(1)/((x-3)^(3))(g(4)=1)`
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