Simplifying
4x3 + -81x = 0
Reorder the terms:
-81x + 4x3 = 0
Solving
-81x + 4x3 = 0
Solving for variable 'x'.
Factor out the Greatest Common Factor (GCF), 'x'.
x(-81 + 4x2) = 0
Factor a difference between two squares.
x((9 + 2x)(-9 + 2x)) = 0
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:
Simplifying
x = 0
Solving
x = 0
Move all terms containing x to the left, all other terms to the right.
Simplifying
x = 0
Subproblem 2
Set the factor '(9 + 2x)' equal to zero and attempt to solve:
Simplifying
9 + 2x = 0
Solving
9 + 2x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-9' to each side of the equation.
9 + -9 + 2x = 0 + -9
Combine like terms: 9 + -9 = 0
0 + 2x = 0 + -9
2x = 0 + -9
Combine like terms: 0 + -9 = -9
2x = -9
Divide each side by '2'.
x = -4.5
Simplifying
x = -4.5
Subproblem 3
Set the factor '(-9 + 2x)' equal to zero and attempt to solve:
Simplifying
-9 + 2x = 0
Solving
-9 + 2x = 0
Move all terms containing x to the left, all other terms to the right.
Add '9' to each side of the equation.
-9 + 9 + 2x = 0 + 9
Combine like terms: -9 + 9 = 0
0 + 2x = 0 + 9
2x = 0 + 9
Combine like terms: 0 + 9 = 9
2x = 9
Divide each side by '2'.
x = 4.5
Simplifying
x = 4.5
Solution
x = {0, -4.5, 4.5}
Свойства функции y=cosx
1. Область определения — все действительные числа (множество R).
2. Множество значений — промежуток [−1;1].
3. Функция y=cosx имеет период 2π.
4. Функция y=cosx является чётной.
5. Нули функции: x=π2+πn,n∈Z;
наибольшее значение равно 1 при x=2πn,n∈Z;
наименьшее значение равно −1 при x=π+2πn,n∈Z;
значения функции положительны на интервале (−π2;π2), с учётом периодичности функции на интервалах (−π2+2πn;π2+2πn),n∈Z;
значения функции отрицательны на интервале (π2;3π2), с учётом периодичности функции на интервалах (π2+2πn;3π2+2πn),n∈Z.
6. Функция y=cosx:
- возрастает на отрезке [π;2π], с учётом периодичности функции на отрезках [π+2πn;2π+2πn],n∈Z;
- убывает на отрезке [0;π], с учётом периодичности функции на отрезках [2πn;π+2πn],n∈Z.