What will be the minima for the function f(x) = x4 – 8x3 + 22x2 – 24x + 8?

What will be the minima for the function f(x) = x4 – 8x3 + 22x2 – 24x + 8? Correct Answer 3

We have, x4 – 8x3 + 22x2 – 24x + 8 ……….(1) Differentiating both sides of (1) with respect to x, we get, f’(x) = 4x3 – 24x2 + 44x – 24 and f”(x) = 12x2 – 48x + 44 ……….(2) At an extremum of f(x), we have f’(x) = 0 Or 4x3 – 24x2 + 44x – 24 = 0 Or x2(x – 1) – 5x(x – 1) + 6(x – 1) = 0 Or (x – 1)(x2 – 5x + 6) = 0 Or (x – 1)(x – 2)(x – 3) = 0 So, x = 1, 2, 3 Now, f”(x) = 12x2 – 48x + 44 f”(1) = 8 > 0 f”(2) = -4 < 0 f”(3) = 8 < 0 So, f(x) has minimum at x = 1 and 3.