Review for Unit 4 Quiz

1

• -infinity

• -1

• 0

• 1

• infinity

3

• 0

• 1/8

• 1/4

• 1

• nonexistant

10

• 0

• 1

• e

• k!

• nonexistent

11

• -1/2

• 0

• 1/2

• 1

• nonexistent

13

• 0

• e^9/9

• 3e^9

• 6e^9

• nonexistent

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

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 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).