Rolle's Theorem & mean value theorem

The value of c guaranteed to exist by the MVT for  $f\left(x\right)=x^2$  on the interval [0,3] is:

• 1

• 2

• 3/2

• 1/2

 $f\left(x\right)=\left(x+3\right)\left(x-1\right)^2,\ \ \ \ \left[-3,1\right]$  

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

• -1

• 5/3

• 3/5

• Rolle's Theorem doesn't apply

 $f\left(x\right)=\left(x-3\right)\left(x+1\right)^2,\ \ \ \ \left[-1,3\right]$  

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

 $f\left(x\right)=x^3+2x,\ \ \ \left[-1,1\right]$  


Find the value of c guaranteed by the Mean Value Theorem.

• 1/√3

• -1/√3

• ±1/√3

• The MVT doesn't apply

Tags

CCSS.HSF.IF.B.6

The value of c guaranteed to exist by the MVT for  $f\left(x\right)=x^2$  on the interval [0,3] is:

• 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]

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Pick a function which is continuous in the given interval.

• y = cot(x) [-π,2π]

• y = $\frac{x^2+5x+3}{x-1}\ \ \ \ \ \ \left[0,3\right]$

• y = $\left(7x^2+6x-3\right)\left(x^6-3x+7\right)\ \ \ \ \ \ \ \ \left[2,9\right]$

• y = $\frac{\sin\left(x\right)}{x-1}\ \ \ \ \ \ \ \ \ \left[0,4\right]$

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.

Tags

CCSS.HSG.GPE.B.5