Consider a continuous function with the following properties: $f(0)=4$ $\left|f^{\prime}(x)\right|

Question

Consider a continuous function with the following properties:  $f(0)=4$  $\left|f^{\prime}(x)\right|<0.5$  $f^{\prime \prime}(x)<0$ for $x<0$  $f^{\prime}(1)=0$ . Which of the following is true?
A)The graph must have a local maximum for $x<0$ . 
B)The graph must not have a local maximum for $x<0$ . 
C)The graph may or may not have a local maximum for $x<0$ .

Quizplus · Accepted Answer

The Answer of Consider a continuous function with the following properties:  $f(0)=4$  $\left|f^{\prime}(x)\right|<0.5$  $f^{\prime \prime}(x)<0$ for $x<0$  $f^{\prime}(1)=0$ . Which of the following is true?
A)The graph must have a local maximum for $x<0$ . 
B)The graph must not have a local maximum for $x<0$ . 
C)The graph may or may not have a local maximum for $x<0$ .

Consider a Continuous Function with the Following Properties f(0)=4f(0)=4f(0)=4 ∣f′(x)∣<0.5\left|f^{\prime}(x)\right|<0.5∣f′(x)∣<0.5 f′′(x)<0f^{\prime \prime}(x)<0f′′(x)<0

Consider a Continuous Function with the Following Properties $f(0)=4$ $\left|f^{\prime}(x)\right|<0.5$ $f^{\prime \prime}(x)<0$