The function f (x) = x (x2 – 4)n (x2 – x + 1), n Ïµ N assumes a local minima at x = 2, then
‘n’ can be any even number
When we differentiate it less than n times there will be a factor or (x – 2) in every for n1.
If we differentiate in n times, only term, with no factor of (x – 2) is one is which (x – 2)n is differention n times
So if x = 2 is a minima, n must be even.
Critical points: x = 2, 0, –2.
At x = 2; we have a local extremes if
x = 2 is a double or ever root ⇒ x Ïµ even.
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A, B > 0, then minimum value of sec A + sec B is equal to
f (x) = x2 – 4 | x | and
Then f (x) has
If xy = 10, then minimum value of 12x2 + 13y2 is equal to