Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Applications of Derivatives

Question:

If $f'(x)=(x-a)^{2 n}(x-b)^{2 m+1}$ where m, $n \in N$, then

Options:

x = a is a point of minimum

x = a is a point of maximum

x = a is not a point of maximum or minimum

None of these

Correct Answer:

x = a is not a point of maximum or minimum

Explanation:

f'(x) = (x – a)2n (x – b)2m + 1

∴  f'(x) = 0 ⇒ x = a, b

f'(x) does not change sign while passing through x = a. Hence 'a' is neither a point of maximum nor a point of minimum.