+0  
 
0
232
3
avatar+80 

x^4-10x^2+9

is there two relative minimums or only one

gadzooks1753  Nov 14, 2017
 #1
avatar+771 
+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+80 
+1

thanks

gadzooks1753  Nov 14, 2017
 #3
avatar+87604 
+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

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