Calculus Theorems

Does the mean value theorem apply to g on [- 2, 5]

• yes

• no

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.B.5

CCSS.HSF.IF.C.7

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

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.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) = x² - 3x - 28,  [-4,7]

• 1.5
• -1.5
• 0.5
• -0.5

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4

Let f be the function defined by f(x) = x³+x-4. What is the value of c for which the instantaneous rate of change of f at x=c is the same as the average rate of change of f over [-1, 3]. 

• 0
• 1
• √(2/3)
• √(7/3)

Tags

CCSS.HSF.IF.B.6

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)

The Mean Value Theorem may be applied to which of the following functions over the interval named?

• f (x) = tan(x) over [0, π]
• f(x) = |x| over [-1, 1]
• f(x) =1/x, over [1, 2]
• f(x) = sin(x)/x over [-π, π]

Tags

CCSS.HSF.IF.B.5

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

The function g is continuous on the interval [0, 5] and has select values in the table. The equation g(x) = 1 must have at least 2 solutions in the interval [0, 5] if k = 

• 6
• 2
• 0
• 1

Tags

CCSS.HSA.REI.D.11

CCSS.HSA.REI.D.10

The function f is continuous and differentiable for 0 ≤ x ≤ 8.
If g(0) = 7 and g(8) = -9, which could be false?

• There is a 'c’ (0<c< 8), where g(c) = -1
• There is a 'c' (0<c<8), where g′(c) = -1
• There is a 'c' (0<c<8), where g(c) = -2
• There is a 'c' (0<c<8), where g′(c) = -2

Find the value of c which is guaranteed by Rolle's Theorem.

• -1
• 5/3
• 3/5
• Rolle's Theorem doesn't apply

Tags

CCSS.HSA.REI.D.11

CCSS.HSA.APR.B.3