What Function Has a Local Minimum Value of 1?

TL;DR

The function h(x) has a local minimum value of 1 because it decreases into that value and then increases out of it, confirming it's a minimum point. In contrast, functions f(x) and g(x) do not satisfy this condition as they either remain constant or continue to decrease.

Transcript

Which function has a local minimum with a value of 1? So let's think about this a little bit. So they tell us the x values, and we see x increasing from negative 4 all the way to positive 4. So our x values are increasing. And they give us different functions here. And they essentially say which of these functions have a local minimum value where t... Read More

Key Insights

• ☺️ To find a function with a local minimum value of 1, it's necessary to analyze the behavior of the functions at different x values.
• 😥 A local minimum point occurs when a function decreases into it and then increases out of it.
• 👈 Evaluating the functions at specific x values allows us to examine the trend and identify local minimum points.

Questions & Answers

Q: What does it mean for a function to have a local minimum value?

A local minimum value for a function represents the lowest point in a specific interval, where the function is lower at that point compared to its neighboring points within that interval.

Q: How can we determine if a point is a local minimum for a function?

To determine if a point is a local minimum, we need to check if the function decreases into that point and then increases out of it. If this condition is met, the point can be identified as a local minimum.

Q: Explain the process of evaluating the functions at different x values.

By substituting the given x values into each function, we can determine the corresponding y values. This helps us analyze the behavior of the functions and identify any local minimum points.

Q: Why is h(x) the only function with a local minimum value of 1?

Among f(x), g(x), and h(x), only h(x) satisfies the condition because it decreases as it approaches 1 and then increases afterward. The other functions either increase or decrease continuously, ruling them out as candidates for a local minimum.

Summary & Key Takeaways

• The task is to identify the function among f(x), g(x), and h(x) that has a local minimum value of 1.

• The x values increase from negative 4 to positive 4, and the functions are evaluated at those points.

• Only h(x) satisfies the condition of having a local minimum at 1, as it decreases into it and then increases out of it.