Practice Four Theorem's and Differentiability

The function, F, above satisfies the conclusion of Rolle's Theorem in the interval [a,b] because:

I. F is continuous

II. F is differentiable on (a,b)

III. F(a) = F(b) = 0

• All 3 statements are true

• Only 2 and 3 are true

• Only 1 is true

• None of the statements are true

The relative max of this function occurs when x is what?

• 5

• infinity

• DNE

• 2.5

For what value of c is the Rolle's thm applicable on the given function f(x) = x²-5x+4 [1,4]

• c = 7/2

• c = 5/2

• c = 3/2

• c = 9/2

Verify the M.V Thm.  for y =  $\frac{x^2-1}{x},\ \ \ \left[-1,1\right]$  

• C =  $\frac{\sqrt{5}-2}{3}$  

• C = can't be located

• c is not defined

• Mean Value Theorem is  not applicable

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.8.F.B.4

CCSS.HSF.IF.B.6

The Mean Value Theorem (for derivatives) on [a, b] requires a function to be

• continuous on [a, b] and differentiable on (a, b)

• only differentiable on (a, b).

• only continuous on [a, b].

• integrable on [a, b].

Suppose f is a continuous function containing the ordered pairs shown in the table. On which interval(s) must f attain a value of 5.9? Select all that apply.

• (-3, -2)

• (-2, -1)

• (0, 1)

• (1, 2)

• (2, 3)

Assume f(x) is continuous over the interval [-2, 3]. The function f has at least how many zeros?

• 1

• 2

• 3

• 4

Determine the interval(s) for which the function is continuous. Select all that apply.

• (p, 0)

• [0, q]

• [q, r]

• (r, s)

• (q, s)

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

TRUE OR FALSE?  If f is continuous on [-1,1], f(-1)=4 and f(1)= -2, then there is a zero between -1 and 1.

• TRUE
• FALSE
• CANNOT BE DETERMINED