Home
Help Index
Blog

Extreme Points of biquadratic equations


Extreme points are points in a curve where the function turn around. In continous functions like quadratic functions, biquadratic functions and any other polynomial, the extreme points are where the slope of the functions equal to zero. Since the slope of a function is the differentiation result of a function, we will need to look for where y'(x)=0.




All you have to do is to check the check box titled "Extreme Points" ( see the picture above ). Then click as HTML to tell Orimath Biquadratic Solver to solve the problem for you and tell you the steps required to get the answer.


Purchase BiQuadratic Solver for $8.00

Answer by Orimath Quadratic Solver :
Question Number 4 :
For this function y(x) = x4 - 5x2 + 4 , answer the following questions :

Answer Number 4 :
The equation x4 - 5x2 + 4 = 0 is already in ax4+bx2+c=0 form.
Then we can imply that the value of a = 1, b = -5, c = 4.

y(x) = x4 - 5x2 + 4
y'(x) = 4x3 - 10x
Use the formula y'(x) = 0 , to find the value of x in the QGraph5A.BMP point
We have to find the function y'(x) first
So we get y'(x) = 4x3 - 10x = 0
This cubic equation can be factorized easily to become :
4*x^3 - 10*x = 0
<=> 4x ( x2 - 2.5 ) = 0
<=> 4x ( x -1.58113883008419 ) ( x + 1.58113883008419 )= 0
The function y(x) = x4 - 5x2 + 4 have three extreme points in real Cartesian Coordinate :
( x , y ) = ( 0 , 4 )
( x , y ) = ( 1.58113883008419 , -2.25 )
( x , y ) = ( -1.58113883008419 , -2.25 )

Purchase BiQuadratic Solver for $8.00


Design and Concept By CreArtSolution