Question
Find the minimum or maximum of the function below.
f(x) = 6x2 - 2
A.
maximum of -2
B.
maximum of 6
C.
minimum of -2
D.
minimum of 8
f(x) = 6x2 - 2
A.
maximum of -2
B.
maximum of 6
C.
minimum of -2
D.
minimum of 8
Answers
Answered by
GPT-4o mini
To find the minimum or maximum of the function \( f(x) = 6x^2 - 2 \), we start by noting the structure of the function. This is a quadratic function of the form \( ax^2 + bx + c \), where \( a = 6 \), \( b = 0 \), and \( c = -2 \).
Since the coefficient of \( x^2 \) (which is \( a = 6 \)) is positive, we know that the parabola opens upwards, indicating that the function has a minimum value.
The vertex of the quadratic function, which gives the minimum value, can be found using the formula \( x = -\frac{b}{2a} \). In this case:
\[
x = -\frac{0}{2 \times 6} = 0
\]
Next, we substitute \( x = 0 \) back into the function to find the minimum value:
\[
f(0) = 6(0)^2 - 2 = -2
\]
Thus, the minimum value of the function \( f(x) = 6x^2 - 2 \) is \(-2\).
Considering the given options:
A. maximum of -2
B. maximum of 6
C. minimum of -2
D. minimum of 8
The correct answer is:
**C. minimum of -2**.
Since the coefficient of \( x^2 \) (which is \( a = 6 \)) is positive, we know that the parabola opens upwards, indicating that the function has a minimum value.
The vertex of the quadratic function, which gives the minimum value, can be found using the formula \( x = -\frac{b}{2a} \). In this case:
\[
x = -\frac{0}{2 \times 6} = 0
\]
Next, we substitute \( x = 0 \) back into the function to find the minimum value:
\[
f(0) = 6(0)^2 - 2 = -2
\]
Thus, the minimum value of the function \( f(x) = 6x^2 - 2 \) is \(-2\).
Considering the given options:
A. maximum of -2
B. maximum of 6
C. minimum of -2
D. minimum of 8
The correct answer is:
**C. minimum of -2**.