3.4 concavity PI

For which DOMAIN is the following cubic function Concave DOWN?

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

• No point of inflection 

• Points b and g

• Points  b, f and g

• Points  a, b, c, d, e, f, g, and h

• Points a, c, e, f and h

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

• No point of inflection

• Points K, R, and S.

• Points K and S

• Points P, Q, K, R, S, and T

• Points Q and T

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  $\left(-\infty,\infty\right)$ . with no point of inflection.

Discuss the concavity for the function

 $f\left(x\right)=x^2-10x+24$  
Select ALL the correct answer(s).

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

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

• Concave up in  $\left(-\infty,-6\right)$  

• Concave down in  $\left(-4,\infty\right)$  

• Concave down  in $\left(-6,\ -4\right)$  

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

 $f\left(x\right)=-x^2+7x-10$  
Select ALL the correct answer(s).

• No point of inflection 

• At x = 2

• At x = 5

• At  x = $\infty$  

• At x = 3.5

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

 $f\left(x\right)=x^4-24x^2+11x+40$ 

• Concave up in $\left(-\infty,-2\right)$  and  $\left(2,\infty\right)$ , Concave down in (-2, 2). And points of inflection at x = -2 and 2

• Concave down in $\left(-\infty,-2\right)$  and  $\left(2,\infty\right)$ , Concave up in (-2, 2). And points of inflection at x = -2 and 2

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

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

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

• No point of inflection 

• Points A and B

• Points  A, B and Z

• Points X, A, Y, B, Z

• Points X, Y and Z

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