Question

Решеня y=x^3+6x^2+9x наидити уmin y max пожалуйста

Answer 1

Y`=3x²+12x+9
3(x²+4x+3)=0
x1+x2=-4 U x1*x2=3
1=-3 U x2=-1
         +                  _                  +
------------(-3)---------------(-1)--------------
               max                min
ymax=y(-3)=-27+54-27=0
ymin=y(-1)=-1+6-9=-4

Answer 2

Finding the Minimum and Maximum of the Function y = x^3 + 6x^2 + 9x

To find the minimum and maximum of the function y = x^3 + 6x^2 + 9x, we can use calculus to find the critical points and determine whether they correspond to a minimum or maximum.

Calculating the Derivative

The first step is to find the derivative of the function y = x^3 + 6x^2 + 9x with respect to x.

The derivative of y with respect to x, denoted as y', can be calculated as: y' = 3x^2 + 12x + 9

Finding Critical Points

To find the critical points, we need to solve the equation y' = 0 for x.

Solving 3x^2 + 12x + 9 = 0 gives us the critical points.

Classifying Critical Points

After finding the critical points, we can classify them as either a minimum or maximum by using the second derivative test.

The second derivative of y with respect to x, denoted as y'', can be calculated as: y'' = 6x + 12

Second Derivative Test

We can use the second derivative test to determine whether the critical points correspond to a minimum or maximum.

- If y'' > 0 at a critical point, it corresponds to a minimum. - If y'' < 0 at a critical point, it corresponds to a maximum.

Conclusion

By following these steps, we can find the critical points and determine whether they correspond to a minimum or maximum for the function y = x^3 + 6x^2 + 9x.