Let $f ( x ) = e ^ { x }$ Then which of the following is the largest interval, of those listed, for which $f ^ { \prime } ( x ) < 0$ for all x in that interval?

Question

A) $( - \infty , \infty )$
B) $( - \infty , 0 )$
C) $( 0 , \infty )$
D) $( - \infty , 3 )$
E) $\varnothing$

Quizplus · Accepted Answer

The derivative of $f(x) = e^x$ is $f'(x) = e^x$, which is always positive for all real numbers $x$. Therefore, there is no interval where $f'(x) < 0$.

Let f(x)=exf ( x ) = e ^ { x }f(x)=ex

Let $f ( x ) = e ^ { x }$