Question

The function f(x) = $\frac { \ell \mathrm { n } ( \pi + x ) } { \ell \mathrm { n } ( e + x ) }$ , x ≥ 0 is

• A. Increasing on and decreasing on
• B. Decreasing on $\left[ 0 , \frac { \pi } { e } \right)$ and increasing on $\left[ \frac { \pi } { e } , \infty \right)$
• C. Increasing on [0, ∞)
• D. Decreasing on [0, ∞)

Answer 1

Answer: (D)

Decreasing on [0, ∞)

Answer 2

f '(x) =

Now π + x > e + x ⇒ $\ln \left( \frac { e + x } { \pi + x } \right)$ < 0 f '(x) < 0

thus f(x) is decreasing.