Increasing & Decreasing & the First Derivative Test

If a function's FIRST derivative is negative at a certain point, what does that tell you?

• The function is increasing at that point
• The function is decreasing at that point
• The concavity of the function is up at that point
• The concavity of the function is down at that point

Tags

CCSS.HSF.IF.B.4

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

Tags

CCSS.HSS.ID.C.7

Over what intervals is f(x) decreasing?

• (-∞, -1) ∪ (1, ∞)

• (-∞, -√3) ∪ (0, √3)

• (-1, 1)

• (-√3, 0) ∪ (√3, ∞)

Tags

CCSS.HSA.REI.D.10

Which of the following could be the graph of f ' , the derivative of f ?

• 
• 
• 
• 
• 

Find the critical points of f(x) = 2x⁴- 4x² + 1

• x= 0
• x = -1, 1
• x = -1, 0, 1
• no critical points

Tags

CCSS.HSA.APR.B.3

What are the intervals of the graph increasing for f(x) = 2x⁴- 4x² + 1

• (-1,0)
• (0,1)
• (-∞,-1) and (1,∞)
• (0,1) and (-1,0)

Tags

CCSS.HSG.SRT.C.8

Find the derivative:
y=5x²e^3x

• y'=10xe^3x(2x+3)
• y'=5xe^3x(3x+2)
• y'=10ex^3x(3x+2)
• y'=5xe^3x(2x+3)

Find all values of c that satisfy the MVT for the function on the given interval

f(x) = -x² + 8x - 17 on [2,6]

• c = 2

• c = 3

• c = 4

• c = 6

Tags

CCSS.HSA.REI.D.11

What are the local maxima of this graph?

• local maximum at (2.2, 3.9)
• local maximum at (-8, 5)
• local maximum at (5, -8)⋃(3.9, 2.2)
• local maximum at (-8, 5)⋃(2.2, 3.9)

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

At what x-value(s) does f(x) have a maximum?

• x = -1
• x = 1
• x = 3
• x = -1 and x = 3