GATE 2020 AG – Question 11
The function $f(x)=x^4-4x^3+6x^2-4x+1$ has a
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: (D) Minimum at x=1
Explanation
Factor the polynomial as (x−1)⁴. A fourth power is nonnegative and is zero only at x=1. Hence it has a global minimum at x=1, D. No second-derivative test is needed at the flat minimum.