Calc Review 3 Curve Sketching: Concavity,, Relative Min and Max

 $\left(1,\infty\right)$  Discuss the concavity and the point(s) of inflection (if any) of the function:

 $f\left(x\right)=x^3-3x^2+10$ 

• Concave up in $\left(-\infty,1\right)$ , Concave down in  $\left(1,\infty\right)$   . And the point of inflection at x = 1

• Concave down in $\left(-\infty,1\right)$ , Concave up in  $\left(1,\infty\right)$   . And the point of inflection at x = 1

•  Concave down in  $\left(-\infty,\infty\right)$. with no point of inflection.

• Concave up in $\left(-\infty,1\right)$  and  $\left(1,\infty\right)$. with no point of inflection.

Discuss the concavity for the function:

 $f\left(x\right)=x^3-8x+5$
Select ALL the CORRECT answer(s).

• Concave up in $\left(-\infty,-1\right)$

• Concave down in  $\left(-\infty,1\right)$

• Concave up in  $\left(1,\infty\right)$

• Concave down in  $\left(-1,\infty\right)$

• None of the above

Discuss the concavity and the point(s) of inflection (if any) for the function

 $f\left(x\right)=x^5-5x+2$ 

• Concave down in  $\left(-\infty,0\right)$  Concave up in ( $\left(0,\infty\right)$   ,. And Point of Inflection at x = 0

• Concave up in  $\left(-\infty,0\right)$ Concave down in  $\left(0,\infty\right)$   ,. And Point of Inflection at x = 0
  

• Concave down in $\left(-\infty,0\right)$ and  $\left(0,\infty\right)$    . with no inflection point.

• Concave up in $\left(0,\infty\right)$ and  $\left(0,\infty\right)$    . with no inflection point.

• Concave up  in $\left(-\infty,\ \infty\right)$ with no inflection point.

Discuss the concavity and the point(s) of inflection (if any) for the function 

 $f\left(x\right)=x^6-4x+2$ 

• Concave down in  $\left(-\infty,0\right)$  Concave up in  $\left(0,\infty\right)$   ,. And Point of Inflection at x = 0

• Concave up in  $\left(-\infty,0\right)$ Concave down in  $\left(0,\infty\right)$   ,. And Point of Inflection at x = 0
  

• Concave down  in $\left(-\infty,0\right)$ and   $\left(0,\infty\right)$  with no inflection point.

• Concave up in  $\left(-\infty,0\right)$  and  $\left(0,\infty\right)$. with no inflection point.

• Concave up  in $\left(-\infty,\ \infty\right)$ with no inflection point.

Find the point(s) of inflection (if it exists) of the graphed function.

• No point of inflection

• Points C, D and E

• Points A, C, E and G

• Points A, B, C, D, E, F and G

• Points B and F

Find the point(s) of inflection (if it exists) of the graphed function.

• No point of inflection

• Points 3 and 5

• Points 1, 3, 5 and 7

• Points 1, 2, 3, 4, 5, 6 and 7

• Points 2, 4 and 6

Discuss the concavity and the point(s) of inflection (if any) of the function:

 $f\left(x\right)=\frac{3x+6}{x-5}$ 

• Concave down in  $\left(-\infty,5\right)$   ,  Concave up  $\left(5,\infty\right)$   in and the point of inflection at x=5
  

• Concave down in $\left(-\infty,5\right)$  and  $\left(5,\infty\right)$    with no point of inflection.

• Concave up in $\left(-\infty,5\right)$  and  $\left(5,\infty\right)$   with no point of inflection.

• Concave up in $\left(-\infty,5\right)$  ,  Concave down in  $\left(5,\infty\right)$   and the point of inflection at x = 5

• Concave up in $\left(-\infty,\infty\right)$ with no point of inflection.

Discuss the concavity and the point(s) of inflection (if any) of the function:

 $f\left(x\right)=\frac{2}{\left(x-1\right)^3}$ 

• Concave down in  $\left(1,\infty\right)$  , Concave up in $\left(1,\infty\right)$  and the point of inflection at x=1.
  

• Concave up in  $\left(-\infty,1\right)$   , Concave down in $\left(1,\infty\right)$ and the point of inflection at x=1.
  

• Concave down in  $\left(-\infty,1\right)$   and $\left(1,\infty\right)$ , with no point of inflection.
  

• Concave up in  $\left(-\infty,1\right)$    and $\left(1,\infty\right)$ , with no point of inflection.

• Concave up in $\left(-\infty,\infty\right)$ with no point of inflection.