Question

F(x) = x² + 3x + 5​

Answer 1

Ответ:

f'(x)=2x+3+0

f'(x)=2x+3

Answer 2

The given expression is a quadratic function of the form:

F(x) = x² + 3x + 5

This function represents a parabola that opens upward because the coefficient of the x² term (which is 1) is positive. To find the vertex, we can use the formula:

x = -b / (2a)

where a is the coefficient of the x² term (1 in this case) and b is the coefficient of the x term (3 in this case).

Using the formula, we have:

x = -3 / (2*1) x = -3/2

To find the y-coordinate of the vertex, substitute the x-coordinate (-3/2) into the function:

F(-3/2) = (-3/2)² + 3(-3/2) + 5 F(-3/2) = 9/4 - 9/2 + 5 F(-3/2) = 9/4 - 18/4 + 20/4 F(-3/2) = 11/4

So, the vertex of the parabola is (-3/2, 11/4).

The value of F(x) is determined by substituting x into the function. For any given value of x, you can substitute it into the function and evaluate the expression. For example, if you want to find the value of F(2), substitute x = 2 into the function:

F(2) = (2)² + 3(2) + 5 F(2) = 4 + 6 + 5 F(2) = 15