At what value of x could the function f(x) = $\frac { \ln x + x } { x }$ have a possible relative maximum or minimum?
A) x = 1
B) x = $e ^ { 2 }$
C) x = $\frac { 1 } { e }$
D) x = e
E) none of these
Differentiate.

Question

Quizplus · Accepted Answer

To find the critical points where a relative maximum or minimum could occur, we differentiate the function f(x) = $\frac{\ln x + x}{x}$. The derivative is f'(x) = $\frac{1 - \ln x}{x}$. Setting f'(x) = 0 gives 1 - $\ln x$ = 0, which implies $\ln x = 1$. Solving for x gives x = e.

At What Value of X Could the Function F(x) = ln⁡x+xx\frac { \ln x + x } { x }xlnx+x​

At What Value of X Could the Function F(x) = $\frac { \ln x + x } { x }$