Question
Question: The function f(x) = x(x<sup>2</sup> – 4)<sup>n</sup>(x<sup>2</sup> – x +1), n ∈ N assumes a local mi...
The function f(x) = x(x2 – 4)n(x2 – x +1), n ∈ N assumes a local minima at x = 2 then
A
'n' can be any odd number
B
'n' can only be an odd prime number
C
'n' can be any even number
D
'n' can only be a multiple of four
Answer
'n' can be any even number
Explanation
Solution
f(2) = 0, f(2 + 0) = positive f(2 − 0) = (−ve)n. If x = 2 is point of local minima then f(2 − 0) > 0
⇒ n = even.