+0

# x^4-10x^2+9

0
93
3
+80

x^4-10x^2+9

is there two relative minimums or only one

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#1
+681
+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.

#2
+80
+1

thanks

#3
+81027
+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

CPhill  Nov 14, 2017

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