11.a. Find the open intervals on which the function is increasing and those on which it is decreasing.b. Identify the function's local extreme values, if any, saying where they occur.410H(t)=8a. On what open interval(s), if any, is the function increasing? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.O A. The function H is increasing on the open interval(s)(Type your answer in interval notation. Use a comma to separate answers as needed.)O B. The function is never increasing.On what open interval(s), if any, is the function decreasing? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.O A. The function H is decreasing on the open interval(s)(Type your answer in interval notation. Use a comma to separate answers as needed.)B. The function is never decreasing.b. Find each local maximum, if any. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.O A. The function has a local maximum at one value of t. The maximum value is H(Type integers or simplified fractions.)O B. The function has a local maximum value at two values of t. In increasing order of t-value, the maximum values are Hand H(Type integers or simplified fractions.)C. The function has a local maximum value at three values of t. In increasing order of t-value, the maximum values are Hн(, н(and=(Type integers or simplified fractions.)D. There are no local maxima.Find each local minimum, if any. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.O A. The function has a local minimum at one value of t. The minimum value is H((Type integers or simplified fractions.), н(O B. The function has a local minimum value at three values of t. In increasing order of t-value, the minimum values are Hand=Н(Type integers or simplified fractions.)O C. The function has a local minimum value at two values of t. In increasing order of t-value, the minimum values are Hand H(Type integers or simplified fractions.)O D. There are no local minima

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Asked Oct 28, 2019

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11.
a. Find the open intervals on which the function is increasing and those on which it is decreasing.
b. Identify the function's local extreme values, if any, saying where they occur.
4
10
H(t)=8
a. On what open interval(s), if any, is the function increasing? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The function H is increasing on the open interval(s)
(Type your answer in interval notation. Use a comma to separate answers as needed.)
O B. The function is never increasing.
On what open interval(s), if any, is the function decreasing? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The function H is decreasing on the open interval(s)
(Type your answer in interval notation. Use a comma to separate answers as needed.)
B. The function is never decreasing.
b. Find each local maximum, if any. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
O A. The function has a local maximum at one value of t. The maximum value is H
(Type integers or simplified fractions.)
O B. The function has a local maximum value at two values of t. In increasing order of t-value, the maximum values are H
and H
(Type integers or simplified fractions.)
C. The function has a local maximum value at three values of t. In increasing order of t-value, the maximum values are H
н(
, н(
and
=
(Type integers or simplified fractions.)
D. There are no local maxima.
Find each local minimum, if any. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
O A. The function has a local minimum at one value of t. The minimum value is H(
(Type integers or simplified fractions.)
, н(
O B. The function has a local minimum value at three values of t. In increasing order of t-value, the minimum values are H
and
=
Н
(Type integers or simplified fractions.)
O C. The function has a local minimum value at two values of t. In increasing order of t-value, the minimum values are H
and H
(Type integers or simplified fractions.)
O D. There are no local minima
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11. a. Find the open intervals on which the function is increasing and those on which it is decreasing. b. Identify the function's local extreme values, if any, saying where they occur. 4 10 H(t)=8 a. On what open interval(s), if any, is the function increasing? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The function H is increasing on the open interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.) O B. The function is never increasing. On what open interval(s), if any, is the function decreasing? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The function H is decreasing on the open interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.) B. The function is never decreasing. b. Find each local maximum, if any. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The function has a local maximum at one value of t. The maximum value is H (Type integers or simplified fractions.) O B. The function has a local maximum value at two values of t. In increasing order of t-value, the maximum values are H and H (Type integers or simplified fractions.) C. The function has a local maximum value at three values of t. In increasing order of t-value, the maximum values are H н( , н( and = (Type integers or simplified fractions.) D. There are no local maxima. Find each local minimum, if any. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The function has a local minimum at one value of t. The minimum value is H( (Type integers or simplified fractions.) , н( O B. The function has a local minimum value at three values of t. In increasing order of t-value, the minimum values are H and = Н (Type integers or simplified fractions.) O C. The function has a local minimum value at two values of t. In increasing order of t-value, the minimum values are H and H (Type integers or simplified fractions.) O D. There are no local minima

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Step 1

Given function is

4
...1)
5
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4 ...1) 5

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Step 2

To find out open intervals on which the function is increasing and those on which it is decreasing

And identify the local extreme values of the function, if any

Step 3

First find out the critical points and the interval

Diff...

4x10
H (t) 8t
5
Н () — 87- 8°
Н () 3D0
8 89 0
8t' (1-2)0
8t = 0
>t 0
or
(1- 0
>-1-0
t1,1
therefore critical points are
t-1,0,1
and interval is
30-1),(-1,0).(0,1) and (1,00)
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4x10 H (t) 8t 5 Н () — 87- 8° Н () 3D0 8 89 0 8t' (1-2)0 8t = 0 >t 0 or (1- 0 >-1-0 t1,1 therefore critical points are t-1,0,1 and interval is 30-1),(-1,0).(0,1) and (1,00)

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