The given function f(x) = |x + 3| has both an absolute maximum and an absolute minimum.
What do you mean by absolute maximum and minimum ?
A function has largest possible value at an absolute maximum point, whereas its lowest possible value can be found at an absolute minimum point.
It is given that function is f(x) = |x + 3|.
We know that to check if function is absolute minimum or absolute maximum by putting the value of modulus either equal to zero or equal to or less than zero and simplify.
So , if we put |x + 3| = 0 , then :
± x + 3 = 0
±x = -3
So , we can have two values of x which are either -3 or 3.
The value 3 will be absolute maximum and -3 will be absolute minimum.
Therefore , the given function f(x) = |x + 3| has both an absolute maximum and an absolute minimum.
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Answer: 1. muiltply the two volumes 2. 273.32 cubic centimeters are your answers hopefully I'm correct on this.
The sides of the triangle are given as 1, x, and x².
The principle of triangle inequality requires that the sum of the lengths of any two sides should be equal to, or greater than the third side.
Consider 3 cases
Case (a): x < 1,
Then in decreasing size, the lengths are 1, x, and x².
We require that x² + x ≥ 1
Solve x² + x - 1 =
x = 0.5[-1 +/- √(1+4)] = 0.618 or -1.618.
Reject the negative length.
Therefore, the lengths are 0.382, 0.618 and 1.
Case (b): x = 1
This creates an equilateral triangle with equal sides
The sides are 1, 1 and 1.
Case (c): x>1
In increasing order, the lengths are 1, x, and x².
We require that x + 1 ≥ x²
Solve x² - x - 1 = 0
x = 0.5[1 +/- √(1+4)] = 1.6118 or -0.618
Reject the negative answr.
The lengths are 1, 1.618 and 2.618.
Answer:
The possible lengths of the sides are
(a) 0.382, 0.618 and 1
(b) 1, 1 and 1.
(c) 2.618, 1.618 and 1.
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