How to find increasing and decreasing intervals of a biquadratic function?

AI Thread Summary
To determine the increasing and decreasing intervals of the biquadratic function y = -x^4 + 18x^2 + 11, one must first find the first derivative, f'(x), and identify critical points. Creating a sign chart for the first derivative will provide clarity on the function's behavior. The resulting third-order equation from setting the first derivative to zero can be solved to find critical points, including a local minimum at zero. This method is effective and straightforward for analyzing the function's intervals. Understanding these intervals is crucial for graphing and interpreting the function's characteristics.
courtrigrad
Messages
1,236
Reaction score
2
Hello all

Given y = -x^4 + 18x^2 + 11 how would you find the intervals where the function is increasing and decreasing? Would you have to find f'(x) and find critical points?

Thanks
 
Physics news on Phys.org
Yep, that's the most straightforward and surefire way to do it.
 
yes that is the way to go...

make a sign chart of the first derivative and you'll have all the info you need

marlon
 
Due to the biquadratic character of the function,the resulting 3-rd order equation (when setting the first derivative to zero) can be solved easily.
One of the solutions is zero and is a local minimum.

Daniel.
 

Thread 'Rolling without slipping on a curved surface'

Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
View full post »
Thread 'Voltmeter readings for this circuit with switches'

Thread 'Voltmeter readings for this circuit with switches'

TL;DR Summary: I would like to know the voltmeter readings on the two resistors separately in the picture in the following cases , When one of the keys is closed When both of them are opened (Knowing that the battery has negligible internal resistance) My thoughts for the first case , one of them must be 12 volt while the other is 0 The second case we'll I think both voltmeter readings should be 12 volt since they are both parallel to the battery and they involve the key within what the...
View full post »
Thread 'Trying to understand the logic behind adding vectors with an angle between them'

Thread 'Trying to understand the logic behind adding vectors with an angle between them'

My initial calculation was to subtract V1 from V2 to show that from the perspective of the second aircraft the first one is -300km/h. So i checked with ChatGPT and it said I cant just subtract them because I have an angle between them. So I dont understand the reasoning of it. Like why should a velocity be dependent on an angle? I was thinking about how it would look like if the planes where parallel to each other, and then how it look like if one is turning away and I dont see it. Since...
View full post »

Similar threads

Finding Absolute Minima & Maxima of a Function
Replies
8
Views
2K
Finding Maximum Number of Interference Maxima?
Replies
3
Views
10K
B How Does Setting x=a Identify Minima or Maxima in Circular Equations?
Replies
10
Views
3K
Finding second furthest distance of const interference from 2 sources
Replies
6
Views
1K
Quotient Derivative and Minima Maxima
Replies
6
Views
1K
Intensity for Young’s Double Slit Interference
Replies
9
Views
7K
MHB A Function's Intervals of Increasing/Decreasing, Extrema and Concavity
Replies
25
Views
5K
A Finding Global Minima in Likelihood Functions
Replies
1
Views
2K
Finding the Distance Between Sound and Wave Maxima at a Train Station
Replies
8
Views
2K
Minima and Maxima of a multivariable function....
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top