Question

If ƒ(x) = x(x – 2) (x – 4), 1 ≤ x ≤ 4, then a number satisfying the condition of the mean value theorem is –

• A. 1
• B. 2
• C. 5/2
• D. 7/2

Answer 1

Answer: (A)

1

Answer 2

ƒ′(x) = (x – 2) (x – 4) + x(x – 4) + x (x – 2)

= 3x² – 12x + 8. Also ƒ(4) = 0 and ƒ(1) = 3.

Thus $\frac{ƒ(4) - ƒ(1)}{4 - 1}$ = –1. We must have –1 = ƒ′(x)

⇒ 3x² – 12x + 9 = 0 ⇒ x² – 4x + 3 = 0 ⇒ x = 1 or x = 3.