Question

The function f(x) = x⁵ – 5x⁴ + 5x³ – 1 has-

• A. One minima and two maxima
• B. Two minima and one maxima
• C. Two minima and two maxima
• D. ) One minima and one maxima

Answer 1

)

Sol. f ¢(x) = 5x⁴ – 20x³ + 15x²

f ¢¢(x) = 20x³ – 60x² + 30x

f ¢(x) = 0 Ž x²(x² – 4x + 3) = 0

Ž x²(x – 1)(x – 3) = 0 Ž x = 0, 1, 3

f ¢¢(1) < 0 & f ¢¢(3) = 540 – 540 + 90 > 0

& f ¢¢(0) = 0 & f ¢¢¢(0) ¹ 0

\ Maximum at x = 1 and minimum at x = 3