QuestionFind the value of $x$ where the function $f(x)$ reaches its minimum. Options: A) -5 B) -3 C) -2 D) 3

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is a real-valued function. . The function $f(x)$ is continuous and differentiable.
3. The minimum value of the function $f(x)$ is achieved at a single point in the domain of $f$ .

STEP 2

To find the minimum value of a function, we need to find the $x$ -value at which the function achieves its lowest $y$ -value. This is typically done by finding the derivative of the function and setting it equal to zero to find the critical points. However, in this problem, we are given a graph of the function and a set of possible $x$ -values.

STEP 3

We are given four possible $x$ -values -5, -3, -2, and3. We need to determine which of these $x$ -values corresponds to the minimum $y$ -value of the function.

STEP 4

The user has identified that the function $f(x)$ is at its minimum when $x = -2$ . This means that the $y$ -value of the function is lowest when $x = -2$ .

STEP 5

Without the actual graph, we cannot visually confirm this. However, if the user's observation is correct, then the correct answer is $x = -2$ .
The value of $x$ for which the function $f(x)$ is at its minimum is $x = -2$ .

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