Question

F(x)=2x^2-x x0=1 ,help​

Answer 1

Смотри.........................

Answer 2

To help you with the function F(x) = 2x^2 - x and the point x0 = 1, we'll perform a few tasks:

1. Calculate the value of the function at x0.
2. Find the first derivative of the function.
3. Determine the slope of the tangent line at x0.

Let's start with each step:

1. Calculate the value of the function at x0 = 1:

To do this, simply plug in x0 = 1 into the function F(x):

F(1) = 2(1)^2 - 1 F(1) = 2(1) - 1 F(1) = 2 - 1 F(1) = 1

So, F(1) = 1.

2. Find the first derivative of the function:

To find the first derivative of F(x), we differentiate the function with respect to x:

F'(x) = d/dx [2x^2 - x]

Using the power rule for differentiation:

F'(x) = 2 * d/dx(x^2) - d/dx(x)

Now, applying the power rule:

F'(x) = 2 * 2x - 1 F'(x) = 4x - 1

3. Determine the slope of the tangent line at x0 = 1:

At x0 = 1, the slope of the tangent line is given by the value of the first derivative at x = 1, i.e., F'(1).

F'(1) = 4 * 1 - 1 F'(1) = 4 - 1 F'(1) = 3

So, the slope of the tangent line at x = 1 is 3.

If you need any further assistance or have any other questions, feel free to ask!