Question
Determine the maximum value
of y=3x2−x
3
A. 0
B. 2
C. 4
D. 6
of y=3x2−x
3
A. 0
B. 2
C. 4
D. 6
Answers
GPT 3.5
To find the maximum value of y, we can take the derivative of y with respect to x and find the critical points.
dy/dx = 6x - 3x^2
Setting the derivative equal to zero, we have:
6x - 3x^2 = 0
Factoring out x, we get:
x(6 - 3x) = 0
Setting each factor equal to zero, we have two critical points:
x = 0 and x = 2
Now, we can find the value of y at these critical points.
For x = 0:
y = 3(0)^2 - 0^3 = 0
For x = 2:
y = 3(2)^2 - 2^3 = 12 - 8 = 4
Comparing the y values at these critical points, we see that the maximum value of y is 4.
Therefore, the answer is C. 4.
dy/dx = 6x - 3x^2
Setting the derivative equal to zero, we have:
6x - 3x^2 = 0
Factoring out x, we get:
x(6 - 3x) = 0
Setting each factor equal to zero, we have two critical points:
x = 0 and x = 2
Now, we can find the value of y at these critical points.
For x = 0:
y = 3(0)^2 - 0^3 = 0
For x = 2:
y = 3(2)^2 - 2^3 = 12 - 8 = 4
Comparing the y values at these critical points, we see that the maximum value of y is 4.
Therefore, the answer is C. 4.