GATE | Sudo GATE 2020 Mock II (10 January 2019) | Question 61

Consider function f(x) = x(x2 – 27) where x is a real number. Then the function has
(A) two minima
(B) two maxima
(C) one minima and one maxima
(D) none of these


Answer: (C)

Explanation: Given function,

f(x) = x(x2-27) 
f'(x) = (x2-27)  + x.2x
3x2 - 27 = 0
x2 - 9 = 0
x = ±3 

And,

f''(x) = 6x 

Check minima and maxima at both the values,

f''(3) 
= 6(3) 
= 18 > 0 
So, minima at x = 3 

Also,

f''(-3) = 6(-3) = -18 < 0 
So, maxima at x = -3 

Option (C) is correct.

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