20. A function f defined on [0, 4] such that f is continuous ey- erywhere, differentiable everywhere except at x = 2, and fails the conclusion of the Mean Value Theorem with a =0 and b = 4. %3D
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![12. Restate the Mean Value Theorem so that its conclusion
248
Chapter 3
Applications of the Derivative
18. Af
tha
tial
of
has to do with tangent lines.
In Exercises 13–22, sketch the graph of a function that satisfies
the given description. Label or annotate your graph so thát it
is clear that it satisfies each part of the description.
13. A function that satisfies the hypothesis, and therefore the
conclusion, of Rolle's Theorem on [2, 6].
14. A function that satisfies the hypothesis, and therefore the
conclusion, of the Mean Value Theorem.
19. Af
su
an
the
20. A
er
15. A functionf that satisfies the hypotheses of Rolle's Theo-
rem on [-2, 2] and for which there are exactly three values
Ce (-2,2) that satisfy the conclusion of the theorem.
16. A functionf that satisfies the hypothesis of the Mean
Value Theorem on [0,4] and for which there are exactly
three values ce (0,4) that satisfy the conclusion of the
theorem.
fai
a
21. A
ex
TE
17. A function f that is defined on [-2,2] with f(-2) = f(2) =
O such that f is continuous everywhere, differentiable ev-
erywhere except at x = -1, and fails the conclusion of
Rolle's Theorem.
22. A
ev
%3D
V
Skills
For each graph of f in Exercises 23-26, approximate all the
values x e (0, 4) for which the derivative of f is zero or does
not exist. Indicate whether f has a local maximum, minimum,
or neither at each of these critical points.
33.
35.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7d1caaac-c43d-4e83-9fd2-e96d2e2c94bc%2F6a511ab0-c0bb-4aba-ba6c-0957d011d9ab%2Fo76gna_processed.jpeg&w=3840&q=75)
![sion
%3D
sfies
at it
of Rolle's Theorem.
such that f is continuous everywhere except at x = -1
and differentiable everywhere except at x
the conclusion of Rolle's Theorem.
the
-1, and fails
20. A function f defined on [0, 4] such that f is continuous ey-
erywhere, differentiable everywhere except at x = 2, and
fails the conclusion of the Mean Value Theorem with
a = 0 and b = 4.
the
ies
21. A function f defined on [-3,3] such that f is continu-
ous everywhere except at x = 1, differentiable everywhere
except at x = 1, and fails the conclusion of the Mean Value
Theorem with a = -3 and b = 3.
an
ly
he
22. A function f defined on [-2,01 such that f is continuous
everywhere except at x
except at x = -2, and fails the conclusion of the Meat
Value Theorem with a = -2 and b= 0.
of
-2, differentiable everywhere
33. f(x)
In 2x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7d1caaac-c43d-4e83-9fd2-e96d2e2c94bc%2F6a511ab0-c0bb-4aba-ba6c-0957d011d9ab%2Fli000t_processed.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
