Нужно найти наибольшее значение функции: y=6корней из2cosx+6x-3п/2-9 на отрезке [0; п/3]

-6sqrt(2)sinx+6=0

sinx=sqrt(2)/2

x=п/4

y(0)=6sqrt(2)-9-3п/2< 0

y(п/4)=6+6п/4-3п/2-9=-3

y(п/3)=3sqrt(2)-9-3п/2+2п=3sqrt(2)-9+п/2

6sqrt(2)-9-3п/2-3sqrt(2)+9-п/2=3sqrt(2)-2п< 0

3sqrt(2)-9+п/2+3=3sqrt(2)-6+п/2< 0

y(п/4)=-3 max

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}

1. Найдите сумму бесконечно убывающей геометрической прогрессии 36: 12; 4; ...;

b1=36

b2=12

b3=4

q=b2/b1

s=b1/(1-q)

q=-12/36=-1/3

s=36/(1+1/3)=36/(4/3)=36*3/4=27

ответ: 27

2. Сумма бесконечно убывающей геометрической прогрессии равна 54. Найти, если

Если...? Тут как будто какого-то условия не хватает ((

3. Найдите сумму и первых членов арифметической прогрессии, если а=1, an=200, n=100​

Sn = (a1 + an)/2* n  

a1 = 1  

an = 200

n = 100

S100 = (1 + 200)/2*100 = 201*50 = 10050

ответ: 10050

Объяснение:

Проверь второе задание, там будто реально условия не хватает.