Question

При каком значении с наибольшее значение функции y=-3x^2 + 9x + c равно -5?

Answer 1

1. Найдем производную функции:

y'=-6x+9

2. Найдем критические точки, т.е. приравниваем производную к 0:

-6x+9=0

6x=9

x=1,5

3. Ищем параметр "с", подставив в функцию значение x (критической точки) и y=-5:

-5=-3*1,5^2+9*1,5+c

c=-5+3*1,5^2-9*1,5

c=-5+6,75-13,5=-11,75

Ответ: с=-11,75

Answer 2

To find the value of 'c' for which the function y = -3x^2 + 9x + c has its maximum value and is equal to -5, we need to use calculus. The maximum value of the function occurs at the vertex of the parabola, and the vertex can be found using the formula:

x_vertex = -b / (2a)

where the quadratic function is in the form ax^2 + bx + c. In this case, a = -3, and b = 9.

Let's proceed with the calculation:

1. First, find the x-coordinate of the vertex (x_vertex):

x_vertex = -b / (2a) x_vertex = -9 / (2 * -3) x_vertex = -9 / (-6) x_vertex = 1.5

2. Now, substitute the value of x_vertex back into the original function to find the corresponding y-coordinate (y_vertex):

y_vertex = -3x^2 + 9x + c y_vertex = -3(1.5)^2 + 9(1.5) + c y_vertex = -3(2.25) + 13.5 + c y_vertex = -6.75 + 13.5 + c y_vertex = 6.75 + c

3. We are given that y_vertex (maximum value) is equal to -5, so we can set up the equation:

6.75 + c = -5

4. Now, solve for 'c':

c = -5 - 6.75 c = -11.75

Therefore, when c is equal to -11.75, the function y = -3x^2 + 9x + c has its maximum value of -5.