Question

Ребят можете проверить... Если не правильно исправьте.Найдите промежутки возрастания и убывания функцийf(x)=5x^2-3x+1 f(x)=10x-310x=3x=3:10x=0,3 + +------------------------------> я тут не могу понять где точка возрастает( 0,32) f(x)=4x-5 f(x)=4f(x) возрастает при x Э(принадлежит) (8;-8) 8-это безконечность...Если что не правильно исправьте, и в первом до делать не могу( Заранее Спасибо! 20пнкт за луч. решение

Answer 1

ты знаки не правильно поставил -,+

возрастает [0.3,+oo)

убывает (-oo,0.3]

2) правильно

Answer 2

Finding the Intervals of Increase and Decrease

To find the intervals of increase and decrease for the given functions, we need to analyze the signs of the derivatives of the functions. The derivative of a function tells us whether the function is increasing or decreasing at a particular point.

Let's start with the first function: f(x) = 5x^2 - 3x + 1.

To find the intervals of increase and decrease, we need to find the critical points of the function. Critical points occur where the derivative is either zero or undefined.

The derivative of f(x) = 5x^2 - 3x + 1 is f'(x) = 10x - 3.

To find the critical points, we set f'(x) = 0 and solve for x:

10x - 3 = 0 10x = 3 x = 3/10

So, the critical point is x = 3/10.

Now, let's analyze the intervals of increase and decrease:

1. For x < 3/10: - To determine the sign of f'(x), we can choose a test point, such as x = 0. - Plugging x = 0 into f'(x) = 10x - 3, we get f'(0) = -3. - Since f'(0) < 0, the function is decreasing for x < 3/10.

2. For x > 3/10: - Again, we can choose a test point, such as x = 1. - Plugging x = 1 into f'(x) = 10x - 3, we get f'(1) = 7. - Since f'(1) > 0, the function is increasing for x > 3/10.

Therefore, the function f(x) = 5x^2 - 3x + 1 is decreasing for x < 3/10 and increasing for x > 3/10.

Now, let's move on to the second function: f(x) = 4x - 5.

Since this is a linear function, its derivative is a constant, and it does not change sign. Therefore, the function f(x) = 4x - 5 is either always increasing or always decreasing.

In this case, since the coefficient of x is positive (4 > 0), the function is increasing for all values of x.

To summarize:

- The function f(x) = 5x^2 - 3x + 1 is decreasing for x < 3/10 and increasing for x > 3/10. - The function f(x) = 4x - 5 is always increasing.

I hope this helps! Let me know if you have any further questions.