+0  
 
0
43
3
avatar+45 

x^4-10x^2+9

is there two relative minimums or only one

 
gadzooks1753  Nov 14, 2017
Sort: 

3+0 Answers

 #1
avatar+634 
+2

Here is the graph of it: https://www.desmos.com/calculator/ox7g6zpagq

Notice that it comes down to a point twice, meaning it has 2 relative minimums.

 
AdamTaurus  Nov 14, 2017
 #2
avatar+45 
+1

thanks

 
gadzooks1753  Nov 14, 2017
 #3
avatar+78753 
+1

x^4 - 10x^2 + 9

 

Taking the derivative, we have that

 

4x^3 - 20x  = 0    factoring, we have that

 

4x ( x^2 - 5)  = 0

 

Setting each factor to 0  and solving for x produces

 

x = 0,  x = √ 5,   x = - √ 5

 

Taking the second derivative, we have

 

12x^2 - 20

 

Putting  0  into this produces a negative...so this is a relative max at x =0

Subbing the othertwo values into the second derivative produces positives...so....we have absolute minimums  at  x  = ±√5 

 

 

cool cool cool

 
CPhill  Nov 14, 2017

11 Online Users

avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details