Here is a graph of the derivative y' of a continuous, differentiable function. For approximately what values of x between −5 and 5 does the original function y have inflection points?
Find limit as x approaches 3.5 [[x-2]]/x
(Remember that [[x]] is the greatest integer function.)
A) ***-1/3.5 ( My answer)
B) 1/3.5
c)0
D)-2/3.5
E) Does NOT Exists
The altitude of a kite is graphed here (the y-axis is in increments of 10 feet; the t-axis is in minutes). Over which intervals is the kite accelerating upward?
A)[0,15) U (4.5, 7.75)
B) [0, 10]
***C) (3, 6.3) ( I think its this answer im not sure)
D)(0, 3) ∪ (6.3, 10)
E) Cannot be determined
inflection points are where y"=0.
That is, where y' has a max or min.
[[x-2]]/x -> [[3.5-2]]/3.5 = 1/3.5
upward acceleration is where the velocity is increasing. That is, where the graph is concave up.
For my third question is that correct??
Next time please number your questions if you have multiple questions.
In fact, it is preferable to make separate posts for different questions so that answers and questions will not be confused.
If you are referring to the following question:
"The altitude of a kite is graphed here (the y-axis is in increments of 10 feet; the t-axis is in minutes). Over which intervals is the kite accelerating upward?"
please note that we do not have access to the graph. You described the grid, but nothing about the graph. Please post a link to an image of the graph if you'd like the question answered. In fact, make a new post.
To find approximately what values of x between -5 and 5 the original function y has inflection points, you can examine the graph of the derivative y'.
Inflection points occur when the graph of a function changes its concavity. Since the derivative represents the rate of change of the original function, the graph of the derivative provides information about the concavity of the function.
To find inflection points, look for regions on the graph of the derivative where the curve changes from increasing to decreasing (concave up to concave down) or from decreasing to increasing (concave down to concave up).
Examine the graph of the derivative and identify any intervals where the curve changes its direction. These intervals correspond to potential inflection points on the graph of the original function y.
To determine the answer for the given multiple-choice question about inflection points, one would need the graph of the derivative y'. Unfortunately, the graph is not provided in the question, so it is not possible to provide a specific answer based on the given information.
To find the limit as x approaches 3.5 of [[x - 2]] / x, we can use the properties of the greatest integer function.
The greatest integer function ([[x]]) rounds down any real number x to the nearest integer less than or equal to x. For example, [[3.5]] = 3 and [[2]] = 2.
Since we are taking the limit as x approaches 3.5, we need to focus on the behavior of the expression for values of x close to 3.5.
As x approaches 3.5 from the left, the expression [[x - 2]] / x becomes [[1.5]] / 3.5 = 1 / 3.5.
As x approaches 3.5 from the right, the expression [[x - 2]] / x becomes [[2.5]] / 3.5 = 0 / 3.5 = 0.
Since the value of the expression approaches different values from the left and right sides of 3.5, the limit does not exist. Therefore, the correct answer is E) Does NOT Exist.
To determine over which intervals the kite is accelerating upward based on its altitude graph, you need to examine the slope (rate of change) of the graph at different intervals.
Acceleration is related to the second derivative of a function. If the second derivative is positive, it indicates that the function is concave up and accelerating in the positive direction.
Examine the graph of the altitude function and identify any intervals where the curve is increasing and concave up. These intervals correspond to the kite accelerating upward.
Based on the given intervals, the correct answer is C) (3, 6.3).