Question

F(x)= ½ x⁴ -x² помогите решить задачу, алгебра 10 класс

Answer 1

Ответ:

Объяснение:f(x)'=2x^3-2x

Формулы при изменении(слово забыл, бывает):x'=1 C'=0 (X^n)'=nx^(n-1)

Answer 2

Problem Statement

You are given the function F(x) = ½ + x⁴ - x² and you need to solve a problem related to it.

Solution

To solve the problem, we can use the bisection method, also known as the binary search method. This method is commonly used to find the root of a function within a given interval.

The bisection method works by repeatedly dividing the interval in half and narrowing down the search space until the root is found or a desired level of accuracy is achieved.

Here are the steps to solve the problem using the bisection method:

1. Define the interval [a, b] within which you want to find the root of the function F(x). 2. Calculate the value of F(a) and F(b) to determine if the root lies within the interval. If F(a) * F(b) < 0, then the root exists within the interval. 3. Calculate the midpoint c of the interval using the formula: c = (a + b) / 2. 4. Calculate the value of F(c). 5. Compare the signs of F(c) and F(a). If they have opposite signs, then the root lies between a and c. Set b = c. 6. If the signs of F(c) and F(a) are the same, then the root lies between c and b. Set a = c. 7. Repeat steps 3-6 until the desired level of accuracy is achieved or the root is found. 8. The final value of c will be the approximate root of the function F(x).

Let's apply the bisection method to solve the problem using the given function F(x) = ½ + x⁴ - x².

Example Calculation

Let's solve the problem using an example calculation.

We want to find the root of the function F(x) within the interval [0, 1.25].

1. Interval: [a, b] = [0, 1.25] 2. Calculate F(a) and F(b): - F(0) = ½ + 0⁴ - 0² = ½ - F(1.25) = ½ + (1.25)⁴ - (1.25)² = 2.25 - Since F(a) * F(b) = ½ * 2.25 = 1.125 > 0, the root does not exist within the interval [0, 1.25]. 3. Therefore, we need to choose a different interval that contains the root.

Please note that the given problem statement does not provide a specific problem to solve using the function F(x) = ½ + x⁴ - x². If you have a specific problem or requirement related to this function, please provide more details so that I can assist you further.