Relationships Between f, f', and f''

 $f'\left(x\right)>0$  means....

•  $f\left(x\right)$  is increasing

•  $f\left(x\right)$  is decreasing

•  $f\left(x\right)$  is concave up

•  $f\left(x\right)\$  is concave down

 $f'\left(x\right)<0$  means....

•  $f\left(x\right)$  is increasing

•  $f\left(x\right)$  is decreasing

•  $f\left(x\right)$  is concave up

•  $f\left(x\right)\$  is concave down

 $f''\left(x\right)<0$  means....

•  $f\left(x\right)$  is increasing

•  $f\left(x\right)$  is decreasing

•  $f\left(x\right)$  is concave up

•  $f\left(x\right)\$  is concave down

 $f''\left(x\right)>0$  means....

•  $f\left(x\right)$  is increasing

•  $f\left(x\right)$  is decreasing

•  $f\left(x\right)$  is concave up

•  $f\left(x\right)\$  is concave down

 $f'\left(x\right)$ is increasing means....

•  $f\left(x\right)$  is increasing

•  $f\left(x\right)$  is decreasing

•  $f\left(x\right)$  is concave up

•  $f\left(x\right)\$  is concave down

 $f'\left(x\right)$ is decreasing means....

•  $f\left(x\right)$  is increasing

•  $f\left(x\right)$  is decreasing

•  $f\left(x\right)$  is concave up

•  $f\left(x\right)\$  is concave down

 $f\left(x\right)$ is decreasing means....

•  $f'\left(x\right)>0$  

•  $f'\left(x\right)<0$ 

•  $f''\left(x\right)>0$  

•  $f''\left(x\right)<0\$  

 $f\left(x\right)$ is increasing means....

•  $f'\left(x\right)>0$  

•  $f'\left(x\right)<0$ 

•  $f''\left(x\right)>0$  

•  $f''\left(x\right)<0\$  

 $f\left(x\right)$ is concave up means....

•  $f'\left(x\right)>0$  

•  $f'\left(x\right)<0$ 

•  $f''\left(x\right)>0$  

•  $f''\left(x\right)<0\$  

 $f\left(x\right)$ is concave down means....

•  $f'\left(x\right)>0$  

•  $f'\left(x\right)<0$ 

•  $f''\left(x\right)>0$  

•  $f''\left(x\right)<0\$