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RideAnS [48]
2 years ago
14

What is the local minimum value of the function g(x)=x^4-5x^2+4? (Round answer to the nearest hundredth)

Mathematics
2 answers:
Svetllana [295]2 years ago
7 0
The answer is
g'(x)=<span>4x^3-10x=0 so </span><span>(4x-10)x=0 it is  x= 0 and  x= 5/2
</span>
<span>g(0)=4
</span>
<span>g(5/2)=x^4-5x^2+4=11.81</span>
the minimum is  M(0, 4)

SSSSS [86.1K]2 years ago
6 0
G ( x ) = x ^4 - 5 x² + 4 
g `( x ) = 4 x³ - 10 x
4 x³ - 10 x = 2 x ( 2 x² - 5 ) = 0 ( the local minimum is where the derivative is equal to zero )
x = 0,  
2 x² - 5 = 0
x² = 5/2
x = +/- √(5/2) = +/- 1.58
g ( 0 ) = 4 ( not the local minimum )
g ( √5/2 ) = g ( -√5/2 ) = ( √5/2 )^4 - 5 (√5/2 )² + 4 =
= 2.5 ² - 5 · 2.5 + 4 = 6.25 - 12.5 + 4 = - 2.25
Answer:
The local minimum is :  M ( - 1.58 ,  - 2.25 ) and N ( 1.58,  - 2.25 ). 
 
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