Thms, Antiderivatives, and Riemann Sums Test

Let f be a function that is continuous on the interval (1, 10). If f(2) = -5 , f(5) = 5 and f(9) = -5, which must be true?

I.  f(x) has a least 2 zeros
II.  For some c, 2 < c < 9, f(c) = 3  
III.  The graph of f(x) has a horizontal tangent

• I. only
• I. and II.
• I. , II. and III.
• II. and III.

What is the average rate of change of the function below over the indicated interval?
f(x) = x² - 3x - 28,  [-4,7]

• 0
• 11
• 6
• 66

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Which value is guaranteed by the MVT for the function given: f(x) = x² - 6x + 8 on [0,3]

• f(c) = 10

• f(c) = 4

• f ' (c) = 3

• f ' (c) = 7/3

Can the MVT be applied to the function on the interval?

f(x) = (x - 3)^2/3 on [1,4]

• Yes

• No

Where is the graph continuous yet NOT differentiable?

• x = a, b, c, d
• x = b, c, d
• x = a, b, 
• x = b, d

For a function that is strictly decreasing, a right hand Riemann Sum is which of the following:

• Overestimate
• Underestimate
• Exact Solution
• Unable to Determine

For a function that is strictly increasing, a right hand Riemann Sum is which of the following:

• Overestimate
• Underestimate
• Unable to Determine
• Exact Solution

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

• -1
• -2
• 1/2
• -1/2

Tags

CCSS.HSA.REI.D.10

• 2
• 4
• 5
• 6

• 2/3 x³
• 2x+C
• 4x+C
•  2/3 x³ +C 

Tags

CCSS.HSA.APR.A.1