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What is the smallest sum that can be obtained by adding a positive number and its reciprocal?
let f(x) = x + 1/x ; To find the minimum of f(x), take the derivative and set equal zero, then solve for x.
f'(x) = 1 - 1/(x2) ; set equal to zero and solve for x --> 0 = 1 - 1/(x2) --> x = 1 & -1.
The question asked for a positive number so disregard x=-1.
So f(1) = 1 + 1 = 2. Is it a minimum or maximum, though? When the derivative = 0, the graph is changing from positive slope to negative[a maximum or relative max], or negative slope to positive [a minimum or relative min]. Let's find out.
When x < 1, we have f' = 1 - 1/(x2), where (x2) is smaller than 1, so [1/(x2)] is larger than 1, so the slope is negative (value is decreasing). When x > 1, (x2) is getting larger than 1, so [1/(x2)] is smaller than 1 and the slope is positive (increasing).
So at x =1 is a minimum [check by plugging in x = 1/2 and x = 3/2].
f(1/2) = 1/2 + 2 = 2.5, and f(3/2) = 3/2 + 2/3 = 9/6 + 4/6 = 13/6 = 2.1666 [both are greater than the sum of 2 at x=1]
So sum = 2 is a minimum.
What else can I help you with?
What is positive 6 minus negative 3 equal?
Subtracting a negative number is the same as adding the corresponding positive number:6 - (-3) = 6 + 3Subtracting a negative number is the same as adding the corresponding positive number:6 - (-3) = 6 + 3Subtracting a negative number is the same as adding the corresponding positive number:6 - (-3) = 6 + 3Subtracting a negative number is the same as adding the corresponding positive number:6 - (-3) = 6 + 3
Is subtracting a negative number the same as adding a positive number?
For negatives, two negatives equal a positive & all goes for positive
Adding a force acting in the opposite direction is the same as adding a n number and a n Number?
it is the same as adding a negative number to a positive number
What are the rules for adding positive and negative numbers?
If you are adding a positive number, then this is the same as normal addition. For instance, 4 add positive 5 is 9. negative 1 add positive 8 is 7. If you are adding a negative number, then this is the same as subtracting that number. For instance 6 add negative 1 is 5. negative 7 add negative 2 is negative 9.
When adding two positive rational numbers will the sum always be zero?
No
What is mid range in a number?
Midrange is the quantity obtained by adding the largest and smallest values in a set of numbers and dividing the result by 2.
What numbers are positive integers?
The positive integers are the numbers obtained by (repeatedly) adding 1 to 0 ...... 1, 2, 3, 4, 5 ..... and so forth, endlessly.
Blue colour in glass is obtained by adding?
Cobalt
How is adding to negative integers the same as and different from subtracting two positive integers?
No- adding negative numbers is like adding positive numbesr , except the answer is negative.
When adding two numbers and the signs are positive the sum is what?
Positive.
Is the answer going to be positive or negative if your adding a negative to a positive?
Not necessarily.
What will adding a positive and a negative integer give you?
A positive integer
When adding 2 integers will the answer be positive?
When adding two integers, the answer will be positive if both integers are positive, or if one is negative but its absolute value is smaller than the absolute value of the positive integer.
What do you get when adding double negatives?
A Positive
What is the rule for adding integers with like signs?
positive + positive = positive negitive + negitive = positive negitive + positive = negitive
What is the least common multiple for?
The least common multiple, or LCM, is the smallest positive integer that all the members of a given set of numbers will divide into evenly with no remainder. It is helpful for adding and subtracting unlike fractions.
How is adding polynomials like adding integers?
The numbers can have a positive or negative sign.
