1. ## For what values...

For what values of a and b will the function defined by f(x)=a(x-b ln x)

have f(2)=5 as arelative minimum value.Justify your conclusion.

2. Originally Posted by mathcalculushelp
For what values of a and b will the function defined by f(x)=a(x-b ln x)

have f(2)=5 as arelative minimum value.Justify your conclusion.
first 2 is a relative minimum for the function that mean it is a critical point for the first derivative

$f(x)=a(x-b\ln x)$

$f'(x) = a-\frac{ab}{x}$

$f'(2) = a-\frac{ab}{2} = 0 \Rightarrow b=2$

and you have f(2)=5

$f(2) = 2a -ab\ln(2) =5$

$2a-a(2)\ln(2) =5 \Rightarrow a=\frac{5}{2-2\ln (2)}$