In Exercises 6-7, identify each of the marked points as being an absolute maximum or minimum, a relative maximum or mini- mum, or none of the above. (A point could be more than one.) 6. -2
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.
Hi I only need help answering number 6, 19, and 21. Thank you.
![Problems
(T/2, 1)
1
In Exercises 6–7, identify each of the marked points as being an
absolute maximum or minimum, a relative maximum or mini-
mum, or none of the above. (A point could be more than one.)
-1
(37/2, -1)
6.
12. fx) — х?V4 —х
y
4
6
(부, )
10
B
RD
(4,0)
7.
(0,0)
2
4
Sx x<0
x x> 0
13. f(x) =
8.
(a) Sketch the graph of a function that has a local mini-
1
mum at 3 and is differentiable at 3.
(b) Sketch the graph of a function that has a local mini-
0.5
mum at 3 and is continuous but not differentiable at
3.
(c) Sketch the graph of a function that has a local mini-
-0,5
(0, 0) 0,5
mum at 3 and is not continuous at 3.
-0,5
In Exercises 9-15, evaluate f'(x) at the points indicated in the
graph.
(x x<0
14. f(x) =
9. f(x)
x> 0
x2 + 1
y
1-
(0, 2)
0,5
-1
-0,5
(0, 0) 0,5
-0.5
150
(x – 2)2/3
+1
In x
24. f(x) =
[1, 4).
15. f(x) =
on
25. f(x) = x13 - x
(0, 2].
on
26. Show that 4 is a critical number of f(x) = (x – 4) +7 but
f does not have a relative extreme value at 4.
27. A cubic function is a polynomial of degree 3; that is, it has
the form ax + bx? + cx + d, where a + 0.
(6,1+ )
2
(2, 1)
(a) Show that a cubic function can have 2, 1, or 0 critical
numbers. Give examples and sketches to illustrate
the 3 possibilities.
10
In Exercises 16–25, find the extreme values of the function on
the given interval.
(b) How many local extreme values can a cubic function
have?
16. f(x) = x + x + 4 on
(-1, 2).
9.
17. f(x) — х -
28. Suppose that a and b are positive numbers. Find the ex-
treme values of f(x) = x° (1 – x)° on [0, 1).
30х + 3 on
(0, 6).
18. f(x) = 3 sin x on
[T/4, 27/3).
Review
19. f(x) — х*V4 — х? on
[-2, 2).
3
on
dy
where x'y – yx = 1.
dx'
20. f(x) = x +
[1, 5].
29. Find
30. Find the equation of the line tangent to the graph of x +
y + xy = 7 at the point (1, 2).
21. f(x) =
[-3, 5).
on
x² + 5
22. f(x) — е' сos x
[0, 1].
31. Let f(x) = x³ + x.
on
f(x+s) – f(x)
23. f(x) = e* sin x
[0, 7].
Evaluate lim
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