Finding Extrema

If $x=3$  is a critical point of  $f\left(x\right),$ and  $f''\left(x\right)\ =\ e^{-x}\left(x^2-2x-4\right)$ then $x=3$   is a 

• local maximum

• local minimum

• neither 

If   $x=0.5$  is a critical point of  $f\left(x\right)$  and  $f''\left(x\right)\ =\ \cos^2x\cdot\ln x$  then  $x=0.5$  is a 

• local maximum

• local minimum

• neither

Tags

CCSS.HSF.IF.C.7

If   $x=e$  is a critical point of  $f\left(x\right)$  and  $f''\left(x\right)\ =\ \ln\left(x\right)-1$  then  $x=e$  is a 

• local maximum

• local minimum

• neither

 Which of the following is NOT a critical point of $f\left(x\right)\ =\ e^x\cdot x^2$ ?

•  $x=0$  

•  $x=1$  

•  $x=-2$  

Which of the following are NOT critical points of $f\left(x\right)\ =\ \ln\left(\cos\left(x\right)\right)$ ? 

•  $x=0$  

•  $x=\frac{\pi}{2}$  

•  $x=\pi$  

•  $x=\frac{3\pi}{2}$  

Which of the following are NOT critical points of $f\left(x\right)\ =3^{4^x}$ ?

•  $x=0$  

•  $x=-7$  

•  $x=-\frac{\ln3}{\ln7}$  

•  $x=1$  

 How many critical points does the function $f\left(x\right)\ =\frac{\sin x}{x}$ have (on its entire domain)?

•  $0$  

•  $2$  

•  $\infty$  

•  $f\left(x\right)$  is not differentiable

How many critical points does the function $f\left(x\right)\ =\ e^x\cdot x^3$  have? 

•  $0$  

•  $1$  

•  $2$  

•  $\infty$  

Where does the global maximum of $f\left(x\right)\ =\ e^{-x^2}$  occur on  $\left[-1,2\right]$ ? 

•  $x=-1$  

•  $x=0$  

•  $x=1$  

•  $x=2$  

Where does the global minimum of  $f\left(x\right)\ =\ x^3-6x^2$  occur on the interval $\left[-2,6.5\right]$ ?

•  $x=-2$  

•  $x=0$  

•  $x=4$  

•  $x=6.5$  

Tags

CCSS.HSA.APR.B.3