Complete this ratio table
1 answer:
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Find the critical points of f(y):Compute the critical points of -5 y^2
To find all critical points, first compute f'(y):( d)/( dy)(-5 y^2) = -10 y:f'(y) = -10 y
Solving -10 y = 0 yields y = 0:y = 0
f'(y) exists everywhere:-10 y exists everywhere
The only critical point of -5 y^2 is at y = 0:y = 0
The domain of -5 y^2 is R:The endpoints of R are y = -∞ and ∞
Evaluate -5 y^2 at y = -∞, 0 and ∞:The open endpoints of the domain are marked in grayy | f(y)-∞ | -∞0 | 0∞ | -∞
The largest value corresponds to a global maximum, and the smallest value corresponds to a global minimum:The open endpoints of the domain are marked in grayy | f(y) | extrema type-∞ | -∞ | global min0 | 0 | global max∞ | -∞ | global min
Remove the points y = -∞ and ∞ from the tableThese cannot be global extrema, as the value of f(y) here is never achieved:y | f(y) | extrema type0 | 0 | global max
f(y) = -5 y^2 has one global maximum:Answer: f(y) has a global maximum at y = 0
Answer with Step-by-step explanation:
Let Z be a set of integers
We have to prove that is odd for all value of x
Z.
There are two cases
1.When x is an odd integer number
2.when x is even integer number
1.When x is an odd integer number
When x is positive odd integer
Then is positive odd number (because square of odd positive number is always positive an odd number )
5x is also odd number
-5x -1 = -even number
Suppose x=3
Then -15-1=-16
Odd number - even number=Odd number
Hence , is an odd number .
When x is negative odd number
Then x square is positive odd number and 5x is negative odd term term
Therefore,odd number + odd number -1=Even number -1=Odd number
Hence is an odd number.
2.When x is an even number
When x is positive even number
x square is positive even number and 5x is positive even number
Even number -Even number -1 =Even number -odd number =Odd number
Suppose x=4
=16-20-1=-5=Odd number
When x is negative even number
Then x square is positive even number and 5x is negative even number
=Even number +Even number -1=Even number -1=Odd number
Hence, for all elements of Zis odd.