Mean Value Theorem

• 1

• 2

• 3/2

• 1/2

• -1

• 5/3

• 3/5

• Rolle's Theorem doesn't apply

• -1

• 5/3

• 3/5

• Rolle's Theorem doesn't apply

• 1/√3

• -1/√3

• ±1/√3

• The MVT doesn't apply

• 1

• 2

• 3/2

• 1/2

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

Pick the function which is discontinuous in the given interval.

• y= tan(x) [-π/3, π/3]

• y = sin(x) [-π,2π]

• y= log(x) [-1,1]

• y = 1/x [4,7]

Pick a function which is continuous in the given interval.

• y = cot(x) [-π,2π]

The geometrical interpretation of Rolle's theorem for y = f(x) in [a,b] is there exist

• a point c ∈ (a,b) where tangent when drawn is parallel to X-axis.

• a point c ∈ [a,b] where tangent when drawn is parallel to X-axis

• a point c ∈ (a,b) where tangent when drawn is parallel to the chord joining end points of the curve y = f(x).

• a point c ∈ [a,b] where tangent when drawn is parallel to the chord joining end points of the curve y = f(x).

The geometrical interpretation of Mean Value theorem for the curve y =f(x) defined in [a,b] says ∃(there exists)

• a point c ∈ [a,b] where tangent when drawn is parallel to the chord joining end points of the curve y = f(x).

• a point c ∈ (a,b) where tangent when drawn is parallel to the X-axis.

• a point c ∈ (a,b) where tangent when drawn is parallel to the chord joining end points of the curve y = f(x).

• a point c ∈ [a,b] where tangent when drawn is parallel to the X-axis.