How do you Determine Increases/Decreases in a Function?

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Alberta, Canada located in the Badlands.In summary, the conversation discusses finding where a function increases or decreases. The given function is x^2-4 square root x and its derivative is determined to be 2x-2x^(-1/2). The process of finding where the derivative is 0 or not defined is discussed, and the hometown of Drumheller is mentioned.
  • #1
Bosnrules
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How do you find out were the function increases/ decreases with the function: X^2-4 square root X.

here is what I have gotten so far:
y=x^2-4 square root X
dy/dx=2x-2^-(1/2)
dy/dx=1/(2x-2x^(1/2))



Thanx
 
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  • #2
[tex]y= x^2-4\sqrt{x}= x^2- 4x^{\frac{1}{2}}[/tex]
[tex]y'= 2x- 2x^{-\frac{1}{2}}[/tex]
(which I think is what you meant)
but I have no idea where you got that last formula. If you do write everything as a single fraction, you get
[tex]\frac{2(x^{\frac{3}{2}}-1)}{x^{\frac{1}{2}}}[/tex]

Anyway, you want to first determine where the derivative is 0 or not defined.
[tex]x^{\frac{1}{2}}[/tex] is only defined for x> 0. Where is [tex]x- x^{-\frac{1}{2}= 0? Those points separate the positive real numbers into intervals. Determine on which intervals y' is positive or negative to determine in which intervals y is increasing or decreasing.
 
  • #3
I don't have any help for you, but how do you spell your own hometown wrong?

Drumheller.

For those who don't know, Drumheller is the home of the world famous Royal Tyrell Museum (Dinosaurs).
 

Related to How do you Determine Increases/Decreases in a Function?

1. What is curve sketching in Math 31?

Curve sketching is a technique used in calculus to visually represent the behavior of a function. It involves analyzing the various components of a function, such as its domain, range, critical points, and asymptotes, to draw a graph that accurately represents the function's behavior.

2. Why is curve sketching important in Math 31?

Curve sketching is an essential skill in Math 31 because it allows us to gain a deeper understanding of the behavior of a function. By graphing a function, we can easily identify important features such as local and global extrema, intervals of increase and decrease, and concavity. This information can help us solve problems and make predictions about the behavior of a function.

3. What are the steps involved in curve sketching?

The steps involved in curve sketching include: identifying the domain and range of the function, finding the x- and y-intercepts, determining the intervals of increase and decrease, finding the critical points and inflection points, analyzing the concavity of the function, and sketching the graph using all the information gathered.

4. How do you find critical points in curve sketching?

Critical points are points where the derivative of a function is equal to zero or undefined. To find critical points, we set the derivative of the function equal to zero and solve for the x-values. These x-values represent the critical points. We also need to check for any points where the derivative is undefined, such as points of discontinuity.

5. What are some common mistakes to avoid in curve sketching?

Some common mistakes to avoid in curve sketching include forgetting to check for points of discontinuity, not considering the behavior of the function at the endpoints of the domain, and not accurately labeling the axis and scales on the graph. It's also essential to carefully analyze the concavity of the function and ensure that the graph accurately represents the behavior of the function in all regions of the domain.

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