MVT and IVT Practice

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

Does the IVT apply to the function on the given interval?

f(x) = (x - 2)/(x² - 16) on [2 , 6]

• Yes

• No

Does the IVT apply to the function on the given interval?

f(x) = 1 + x + 3tan(x) on [0 , 1]

• Yes

• No

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

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

• Yes

• No

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

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

Where is the graph continuous yet NOT differentiable?

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

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

Given the function f(x) = x³ + x - 3, which of the intervals below contains a zero?

• [-1,1]
• [0,1]
• [1,2]
• None of these intervals

Given a continuous function on the interval [4,7].  Let's say that f(4) = 10 and f(7) = 20.  Is there a value on the interval [4,7] where f(x) = 15?

• Yes - if the function is continuous, then there must be an x value on that interval that passes through 15 on its way from 10 to 20.
• No because there is no sign change on the interval [4,7].
• No because that would be just too good to be true.
• Yes - at x = 5.5.