Young Olson
04/17/2024 · Primary School
\( f(x)=x^{2} \) if necessary, fill in the answer box to complete your choice. A. The function has a relative minimum and the minimum value is \( \square \) at \( x=\square \). B. The function has no relative minimum.
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Step-by-step Solution
The function \( f(x) = x^2 \) is a quadratic function that opens upwards.
To find the relative minimum, we can analyze the function:
1. The vertex of the parabola represented by \( f(x) = x^2 \) is at the point \( (0, 0) \).
2. Since the parabola opens upwards, the vertex represents the lowest point on the graph.
Thus, the function has a relative minimum at \( x = 0 \), and the minimum value is \( f(0) = 0^2 = 0 \).
So, we can fill in the answer box as follows:
A. The function has a relative minimum and the minimum value is \( 0 \) at \( x = 0 \).
Quick Answer
A. The function has a relative minimum at \( x = 0 \) with a minimum value of \( 0 \).
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