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

Answer: (C)

For n1 = 3, n2 = 5, there exists α ∈ (3, 5) where f attains local maxima.

Answer 2

The correct answer is (C) : For n1 = 3, n2 = 5, there exists α ∈ (3, 5) where f attains local maxima.
For n 2 ∈ odd, there will be local minima in (3, 5)
for n 2 ∈ even, there will be local maxima in (3, 5)