5-1 The Mean Value Theorem

5-1 The Mean Value Theorem

Guided Notes

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Multiple Choice

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

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

*Hint: Example 1 

• -1

• 5/3

• 3/5

• Rolle's Theorem doesn't apply

Multiple Choice

The geometrical interpretation of Mean Value theorem for the curve  $y=f\left(x\right)$   defined in  $\left[a,b\right]$   says  $\in$   (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.

Multiple Choice

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

Multiple Choice

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

Multiple Choice

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


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

• 1/√3

• -1/√3

• ±1/√3

• The MVT doesn't apply

Multiple Choice

Does the mean value theorem apply to f on [0, 5] ?

• yes

• no

Multiple Choice

• YES

• NO

Multiple Choice

• YES

• NO