3.2 Concavity and Inflection point

Find the intervals of concavity for

f(x) = x² + 2x + 1.

• concave up: (-∞,∞)

• concave down: (-∞,∞)

• concave up: (2, ∞)

  concave down: (-∞,2)

• concave up: (-∞,2)

  concave down: (2, ∞)

Find the relative minimum values for f(x)=3x⁴-2x³-9x²

• -1

• 0

• 1.5

• -1 and 1.5

Identify the interval from the derivative graph where the function is concave up.

• (-1,1) & (3,4)
• (-3,-2)
• (-2,-1)
• (-3,-1) & (1,3)

Over what interval(s) is f(x) concave up? (Be careful this is a graph of f'!)

• (-∞, -3)

• (-3, 1)

• (-∞,-3) U (1, ∞)

• (-5, 0)U(2, ∞)

What will be true at an inflection point?  (select the best answer)

• f(x)=0
• f'(x)=0
• f''(x)=0
• The function is undefined

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

$f\left(x\right)=-2x^3-24x^2-14x+5$

• Concave up in $\left(-\infty,-4\right)$ Concave down in $\left(-4,\infty\right)$ , And the point of inflection at x = - 4

• Concave down in $\left(-\infty,-4\right)$ Concave up in $\left(-4,\infty\right)$ , And the point of inflection at x = - 4

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

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