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Local extrema Use the sign pattern for the derivative df/dx=6(x-1)(x-2)^2(x-3)^3(x-4)^4

Local extrema Use the sign pattern for the derivative
df/dx=6(x-1)(x-2)^2(x-3)^3(x-4)^4

Grade:12th pass

2 Answers

Arun
25758 Points
2 years ago
Dear student
 
If we use wavy curve method to check the sign of df/dx
Then we see that in
-infinity to 1 , it is + sign
And 1 to 3 it is negative
Again 3 to infinity it is positive
 
Hence local maximum exist at x = 1
And local minimum exist at x = 3
 
Hope it helps
Vikas TU
14149 Points
2 years ago
Dear student 
Since the second derivative is zero, the function is neither concave up nor concave down at x = 0. It could be still be a local maximum or a local minimum and it even could be an inflection point. Let's test to see if it is an inflection point. We need to verify that the concavity is different on either side of x = 0.
Good Luck 

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