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If we were to graph the number it would be:
y = x
If we were to graph the square it would be:
y = x²
The difference would be:
f(x) = x - x²
You want to maximize this difference, so take the derivative:
f'(x) = 1 - 2x
Then set it to zero:
0 = 1 - 2x
Add 2x to both sides:
2x = 1
Divide both sides by 2:
x = ½
Answer: ½ is the number that most exceeds its square.
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What number exceeds its square by the maximum amount?
If we were to graph the number it would be: y = x If we were to graph the square it would be: y = x² The difference would be: f(x) = x - x² You want to maximize this difference, so take the derivative: f'(x) = 1 - 2x Then set it to zero: 0 = 1 - 2x Add 2x to both sides: 2x = 1 Divide both sides by 2: x = ½ Answer: ½ is the number that most exceeds its square.
Three times the square of a certain positive number exceeds six times the number by nine Find the number?
The problem can be written as3x2 = 6x + 9x is the number we want to findSolution:x2 = 2x + 3x2 - 2x - 3 = 0(x-3)(x+1) = 0x = -1, 3
How do you figure out a number is a square number?
If the square root is an integer, it's a square number.
Is the square root of a positive number an irrational number?
Sometimes the square root of a positive number can be irrational, as in the square root of 2 (which is a non-perfect square number), but sometimes it is a rational number, as in the square root of 25 (which is a perfect square number).
The square of 9 more than a number is equal to 9 more than the square of the number?
The square of 9 more than a number is equal to nine more than the square of a number. What is the number?
