Review for Test 5

Answer yes or no

• yes

• no

Tags

CCSS.HSA.REI.D.10

The Mean Value Theorem applies to f(x) = 3x - x² on the interval [2, 5]. Find the value of x where the slope of the tangent line is equal to the slope of the secant line

• 2

• -4

• 3.5

• -2

Tags

CCSS.HSF.IF.B.6

• Average Rate of Change
• Average Value of f
• Intermediate Value Theorem
• Rolle's Theorem

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.B.6

• Mean value theorem
• Rolle's theorem
• Intermediate Value Theorem
• Fundamental Theorem of Calculus

What is the average rate of change of the function below over the indicated interval?
f(x) = 12√(x),  [1,16]

• 12 / 5
• 1
• 0
• 36

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4

What is x-value at which the function below has the same slope as the average rate of change over the indicated interval?
f(x) = 12√(x),  [1,16]

• 2.5
• 6.25
• 14.4
• 6

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4

On the closed interval [-2,3], the absolute maximum value(s) of f(x) = x³-3x²+12 occurs at x = 

• 0 and 3
• 0
• 0 and 2
• -2 and 0

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.CED.A.1

Suppose that f is differentiable for all reals. For x in the interval (-5, 0), suppose that f'(x)<0. For x in the interval (0, 5), suppose that f'(x) >0. Then at x = 0 it must be true that f has 

• an inflection point
• an absolute maximum
• an absolute minimum
• a relative minimum

Suppose that f is differentiable for all reals. For x in the interval (-∞, 4), suppose that f'(x)>0. For x in the interval (4, ∞), suppose that f'(x) <0. Then at x = 4 it must be true that f has 

• no extrema
• a relative minimum
• an absolute maximum
• an absolute minimum

Let g be a continuous function of the closed interval [-1, 3]. If g(-1)=-10 and g(3) = 6, which of the following are guaranteed? 

• g(0) = 0
• g'(c)= 0 for some c in (-1,3)
• g'(c)= 4 for some c in (-1, 3)
• g(c)= 4 for some c in (-1, 3)