We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
295
2
avatar

The graphs of $y=3-x^2+x^3$ and $y=1+x^2+x^3$ intersect in multiple points. Find the maximum difference between the $y$-coordinates of these intersection points.

 Mar 28, 2018
 #1
avatar+28074 
+3

This graph should help:

 Mar 28, 2018
 #2
avatar+22569 
+1

The graphs of $y=3-x^2+x^3$ and $y=1+x^2+x^3$ intersect in multiple points. Find the maximum difference between the $y$-coordinates of these intersection points.

 

 

\(\begin{array}{|rcll|} \hline 3-x^2+\not{x^3} &=& 1+x^2+ \not{x^3} \\ 3-x^2 &=& 1+x^2 \quad & | \quad -1-x^2 \\ 3-x^2 -1-x^2 &=& 0 \\ 2-2x^2 &=& 0 \\ 2(1-x^2) &=& 0 \quad & | \quad : 2 \\ 1-x^2 &=& 0 \\ x^2 &=& 1 \quad & | \quad \sqrt() \\ x &=& \pm\sqrt{1} \\\\ x_1 &=& 1 \\ y_1 &=& y(1) \\ &=& 1+1+1 \\ \mathbf{y_1 } &\mathbf{=}& \mathbf{3} \\\\ x_2 &=& -1 \\ y_2 &=& y(-1) \\ &=& 1-1+1 \\ \mathbf{y_2} &\mathbf{=}& \mathbf{1} \\ \hline \end{array}\)

 

\(\begin{array}{|rcll|} \hline y_1 - y_2 &=& 3-1 \\ &=& 2 \\ \hline \end{array}\)

 

The maximum difference between the  y-coordinates of these intersection points is 2

 

 

 

laugh

 Mar 28, 2018

14 Online Users

avatar
avatar
avatar