First and Second Derivative Practice

Over what interval(s) is f(x) decreasing?

• (-3, 1)
• (-∞, -5) ∪ (0, 2)
• (-∞, -3) ∪ (1, ∞)
• (-5, 0) ∪ (2, ∞)

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

Tags

CCSS.HSF.LE.B.5

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

For a function g(x), g''(3)=-8 indicates that g(x) is ____________ at x=3.

• increasing
• decreasing
• concave up
• concave down

Over what interval(s) is f(x) decreasing?

• (-3, 1)
• (-∞, -5) ∪ (0, 2)
• (-∞, -3) ∪ (1, ∞)
• (-5, 0) ∪ (2, ∞)

Tags

CCSS.HSA.REI.D.10

The function

 $f\left(x\right)=2x^3+x^2-20x+1\$  has a relative minimum at

• -2

• 2

• -5/3

• 1

Consider the function

 $f\left(x\right)=x^3+3x^2-45x+5$  Which statements are true: 

• I 

• II

• III

• None of them 

Consider the function

 $f\left(x\right)=x^3+3x^2-45x+5$  When is the function concave up?

•  $\left(-\infty,-1\right)$  
  

•  $\left(-1,\ \infty\right)$  

•  $\left(-5,3\right)$  
  

•  $\left(-\infty,\ -5\right)$  
  

f'(x) graph is shown in the image above. 𝑓(𝑥) has a local minimum at 𝑥 =

• 1

• 3

• 4

• 5

The graph of f'(x) is shown above. The graph of 𝑓 has a point of inflection at 𝑥 =

• 1 only

• 3 only

• 3 and 4

• none of these