The points (4,t) and (5,-
4) fall on a line with a slope of
-
7. What is the value of t?
t=

Answer:Certainly, let's discuss this in a more comprehensive manner at a college-level.

Option 1: f(x) has a maximum at x = -2

This statement suggests that within the interval -2 ≤ x ≤ 4, the function f(x) attains its highest value at the specific point x = -2. In mathematical terms, it implies that there exists a local maximum at x = -2, where the function experiences a critical point. Critical points are those where the derivative of the function is equal to zero, indicating a potential extremum (maximum or minimum). In this case, a maximum is asserted at x = -2, which means that as we approach this point from both the left and the right, the function increases, but as we move away from x = -2, it starts to decrease. It's important to note that this assertion is based on the assumption that the function possesses a local maximum at this specific x-value.

Option 2: f(x) increases

Option 2 claims that the function f(x) displays a continuous and consistent increase throughout the entire interval from -2 to 4. This means that as we progress from any value on the left side of the interval to any value on the right side, the function's output monotonically and steadily grows. There is no specific point within this interval where the function reaches a maximum; instead, it is characterized by an upward trend. This assertion aligns with the concept of a monotonically increasing function, where the derivative is non-negative or greater than zero over the entire interval. In essence, Option 2 posits that there is no local maximum within the specified range, and the function simply increases without reaching a peak.

To conclusively determine which option is valid, it's imperative to analyze the specific mathematical expression or data representing the function f(x) within the interval -2 ≤ x ≤ 4. A critical examination of the function's behavior, which can be ascertained from its graph, its derivative, or its rate of change, would provide concrete evidence as to whether it exhibits a maximum at x = -2 or continuously increases throughout the interval. Additionally, considering the context and nature of the function is essential in making an informed determination, as some functions may inherently possess certain characteristics that lead to either a local maximum or continuous growth.

Step-by-step explanation: give me brainlest pls

Answer:

Option 1: f(x) has a maximum at x = -2 is the correct answer.

Step-by-step explanation:

To determine whether each function on the interval -2 ≤ x ≤ 4 has a maximum at x=-2 or increases, we need to analyze the behavior of the function.

Let's start with Option 1: f(x) has a maximum at x = -2. In this case, if the function has a maximum at x = -2, it means that the function reaches its highest point at x = -2 and then decreases as we move away from that point.

Now let's consider Option 2: f(x) increases. If the function increases, it means that the function is getting larger as we move along the x-axis from left to right.

To determine whether each function has a maximum at x = -2 or increases, we need to analyze the behavior of the function on the given interval.

For example, let's say we have a function f(x) = x^2. If we plug in values within the given interval, we can observe the behavior of the function:

f(-2) = (-2)^2 = 4

f(0) = (0)^2 = 0

f(4) = (4)^2 = 16

From these calculations, we can see that the function f(x) = x^2 has a maximum at x = -2, as f(-2) = 4, and then it decreases as we move away from x = -2.

Therefore, for this specific function, Option 1: f(x) has a maximum at x = -2 is the correct answer.

To determine the behavior of other functions on the given interval, you will need to analyze their equations and calculate the corresponding values within the interval. By doing so, you can identify whether each function has a maximum at x = -2 or increases.

Remember, it is essential to consider the behavior of the function within the given interval to accurately determine whether it has a maximum at x = -2 or increases.