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A) Find the value of 8^1/3 b) Find the value of 8^2/3 c) Find the value of 16^3/4
1 answer:
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Answer:
Where 0 < x < 3
The location of the local minimum, is (2, 0)
The location of the local maximum is at (0, 16)
Step-by-step explanation:
The given function is f(x) = (x + 2)⁴
The range of the minimum = 0 < x < 3
At a local minimum/maximum values, we have;
∴ (-x + 2)³ = 0
x = 2
When x = 2, f''(2) = -12×(-2 + 2)² = 0 which gives a local minimum at x = 2
We have, f(2) = (-2 + 2)⁴ = 0
The location of the local minimum, is (2, 0)
Given that the minimum of the function is at x = 2, and the function is (-x + 2)⁴, the absolute local maximum will be at the maximum value of (-x + 2) for 0 < x < 3
When x = 0, -x + 2 = 0 + 2 = 2
Similarly, we have;
-x + 2 = 1, when x = 1
-x + 2 = 0, when x = 2
-x + 2 = -1, when x = 3
Therefore, the maximum value of -x + 2, is at x = 0 and the maximum value of the function where 0 < x < 3, is (0 + 2)⁴ = 16
The location of the local maximum is at (0, 16).
Given:
The first two terms in an arithmetic progression are -2 and 5.
The last term in the progression is the only number in the progression that is greater than 200.
To find:
The sum of all the terms in the progression.
Solution:
We have,
First term :
Common difference :
nth term of an A.P. is
where, a is first term and d is common difference.
According to the equation, .
Divide both sides by 7.
Add 1 on both sides.
So, least possible integer value is 30. It means, A.P. has 30 term.
Sum of n terms of an A.P. is
Substituting n=30, a=-2 and d=7, we get
Therefore, the sum of all the terms in the progression is 2985.