Intermediate Value Theorem (IVT)

According to the IVT, what value of c fulfills the theorem's guarantee?

• 2

• 3

• 0

• 5

According to the IVT, what value of c fulfills the theorem's guarantee?

• 0

• 2

• 1/2

• 3

Given the function f is continuous on the closed interval [-2, 2], find c such that f(c)=2

• 2

• 1

• -1

• 0

Given the function g is continuous on the closed interval [-1, 4] where g(-1) = -4 and g(4) = 1, which answer is guaranteed by the IVT?

• g(c) = -3 for at least one c between -4 and 1

• g(c) = 3 for at least one c between -1 and 4

• g(c) = 3 for at least one c between -4 and 1

• g(c) = -3 for at least one c between -1 and 4

Given h(x) is continuous on the interval [1,6], which interval(s) must contain a solution to h(x)=0?

• [3,4]

• [4,6]

• [1,3]

• None of these

Given g(x) is continuous on the interval [-2,4], which interval(s) must contin a solution to g(x)=-1?

• [-2,2]

• [0,2]

• [2,4]

• All of the above

Given f(x) is continuous on the closed interval [1,5], where f(1)=1 and f(5)=-3. Which answer is guaranteed by the intermediate value theorem?

• f(c) = 2 for at least one c between -3 and 1

• f(c) = -2 for at least one c between 1 and 5

• f(c) = 2 for at least one c between 1 and 5

• f(c) = -2 for at least one c between -3 and 1

Given that g(x) is continuous on the closed interval [-1, 5], which interval sets must contain a solution to g(x) = 3?

• [2, 4]

• [4, 5]

• [-1, 2]

• None of the above