Question

Let f : R → R be a function defined by:
\(ƒ(x) = (x-3)^{n_1} (x-5)^{n_2} , n_1, n_2 ∈ N\)
Then, which of the following is NOT true?

• A. For n₁ = 3, n₂ = 4, there exists α ∈ (3, 5) where f attains local maxima.
• B. For n₁ = 4, n₂ = 3, there exists α ∈ (3, 5) where f attains local minima.
• C. For n₁ = 3, n₂ = 5, there exists α ∈ (3, 5) where f attains local maxima.
• D. For n₁ = 4, n₂ = 6, there exists α ∈ (3, 5) where f attains local maxima.

Answer 1

The Correct Option is C

The correct answer is (C) : For n₁ = 3, n₂ = 5, there exists α ∈ (3, 5) where f attains local maxima.
For n₂ ∈ odd, there will be local minima in (3, 5)
for n₂ ∈ even, there will be local maxima in (3, 5)