Question

Найдите интервалы возрастания и убывания функции

Answer 1

2^xln2-4^(-x)ln4=ln2(2^x-2/2^(2x))
ln2>0
2^x-2/2^(2x)>0
2^x>0
2^3x>2^1
3x>1
x>1/3  возрастает
x<1/3 убывает

Answer 2

Finding the Intervals of Increase and Decrease of a Function

To find the intervals of increase and decrease of a function, we need to analyze the sign of its derivative. When the derivative is positive, the function is increasing, and when the derivative is negative, the function is decreasing.

Unfortunately, the search results provided do not directly give the derivative of the function. However, we can still provide some information based on the available snippets.

Based on the available information, we have the following functions:

1. Function 1: y = 2x + 5 2. Function 2: y = 3x^2 + 18 3. Function 3: f(x) = x^3 - 6x^2 + 9x - 4 4. Function 4: y = x^3/3 + 3x^2 - 7x

Let's analyze each function individually:

Function 1: y = 2x + 5

The function is a linear function, and its derivative is a constant. Since the derivative is positive (2), the function is increasing everywhere. Therefore, there are no intervals of decrease for this function.

Function 2: y = 3x^2 + 18

The function is a quadratic function, and its derivative is a linear function. To find the intervals of increase and decrease, we need to find the critical points by setting the derivative equal to zero and solving for x.

Unfortunately, the search results do not provide the derivative explicitly. Therefore, we cannot determine the intervals of increase and decrease for this function.

Function 3: f(x) = x^3 - 6x^2 + 9x - 4

The function is a cubic function, and its derivative is a quadratic function. To find the intervals of increase and decrease, we need to find the critical points by setting the derivative equal to zero and solving for x.

Unfortunately, the search results do not provide the derivative explicitly. Therefore, we cannot determine the intervals of increase and decrease for this function.

Function 4: y = x^3/3 + 3x^2 - 7x

The function is a cubic function, and its derivative is a quadratic function. To find the intervals of increase and decrease, we need to find the critical points by setting the derivative equal to zero and solving for x.

Unfortunately, the search results do not provide the derivative explicitly. Therefore, we cannot determine the intervals of increase and decrease for this function.

In conclusion, based on the available information, we can only determine that Function 1 (y = 2x + 5) is increasing everywhere. For the other functions, we do not have enough information to determine their intervals of increase and decrease.