Question

Find the relation between a>0 and b>0 so that...

Answer 1

Find the relation between a>0 and b>0 so that the function:

\[f(x)= \sqrt[a]{x}\ln (bx)\]

has a critical point at x=1 .

Answer 2

Any hints as to how to go about doing this?

Answer 3

@myininaya @hartnn @mahmit2012 @ganeshie8

Answer 4

I am thinking about taking the derivative but I am not sure how that would help...

Answer 5

to get critical point, you take first derivative and equate it to 0

Answer 6

Yeah...

Answer 7

then put x=1

Answer 8

so product and chain rule

Answer 9

I assume a and b would be constants...

Answer 10

yes, they are constants

Answer 11

So I got: