Question

If the function

f(x) = $\left\lbrack \frac{(x - 2)^{3}}{a} \right\rbrack$sin (x – 2) + a cos (x – 2), [.] denotes the

greatest integer function, is continuous and differentiable in

[4, 6], then –

• A. a ∈ [8, 64]
• B. a ∈ (0, 8]
• C. a ∈ [64, ∞)c
• D. None of these

Answer 1

Answer: (C)

a ∈ [64, ∞)c

Answer 2

Since [x³] is not continuous and differentiable at integral point. So f(x) is continuous and differentiable in [4, 6] if

$\frac{(x - 2)^{3}}{a}$ = 0 ⇒ a ≥ 64