Exit Ticket for Day 27 of Calculus
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Becerra Gurrola, Luis
Bennett, Jasmine
Botello, Lisa
Garvin, Andrew
Hooper, Halie
Schminke, Luke
White, Maliah
KEY
1. According to Rolle's Theorem, if f(x₁)=f(x₂), ______.
both x₁ and x₂ are absolute maxima of the function
then x₁ must be equal to x₂
the derivative of f(x) is zero at both x₁ and x₂
there must be some point between x₁ and x₂ where the derivative of f(x) is zero
2. The Mean Value Theorem only applies to a function f(x) over some domain A if ______.
there is at least one value of x in the domain A for which f(x) is not differentiable
f(x) is both continuous and differentiable over the domain A
f(x) has at least one undefined point in the domain A
3. Look at the graph shown below. In red, I've drawn some function, and in purple I have connected the endpoints of this function on the domain [2,2]. What does the Mean Value Theorem tell us about this situation?
There is some value of x between 2 and 2 where the line tangent to f(x) at that point is horizontal.
There is some value of x between 2 and 2 where the line tangent to f(x) at that point is vertical.
There is no value of x between 2 and 2 where the line tangent to f(x) at that point is parallel to the purple line.
There is some value of x between 2 and 2 where the line tangent to f(x) at that point is parallel to the purple line.
These are review questions:
4. What is the derivative of this function?
Option 1
Option 2
Option 3
Option 4
5. Find the derivative of the following function:
Option 1
Option 2
Option 3
Option 4
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