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 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
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
2K
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