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Let f(x) be a function such that f'(a) ≠ 0. Then at x = a,f(x)
- a)cannot have a maximum
- b)cannot have a minimum
- c)must have neither a maximum nor a minimum
- d)none of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Let f(x) be a function such that f'(a) ≠ 0. Then at x = a,f(x)a...
Let f(x) = |x|.
f'(0) ≠ 0 but f(x) has a minimum at x = 0.
f'(0) ≠ 0 but f(x) has a minimum at x = 0.
Most Upvoted Answer
Let f(x) be a function such that f'(a) ≠ 0. Then at x = a,f(x)a...
Explanation:
Nonzero Value at x = a
- Given that f(a) ≠ 0, meaning the function has a nonzero value at x = a.
Understanding Maximum and Minimum Points
- At a maximum point, the derivative of the function changes from positive to negative.
- At a minimum point, the derivative changes from negative to positive.
Analysis of Options
- Option A: Cannot have a maximum: Since f(a) ≠ 0, the function can have a maximum at x = a.
- Option B: Cannot have a minimum: Since f(a) ≠ 0, the function can have a minimum at x = a.
- Option C: Must have neither a maximum nor a minimum: This statement is not true as the function can have a maximum, minimum, or neither at x = a depending on the behavior of the function around that point.
- Option D: None of these: This is the correct answer as the function can have a maximum, minimum, or neither at x = a depending on the function's behavior.
Therefore, the correct answer is option D. None of these. The presence of a nonzero value at x = a does not restrict the function from having a maximum or minimum at that point.
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Let f(x) be a function such that f'(a) ≠ 0. Then at x = a,f(x)a)cannot have a maximumb)cannot have a minimumc)must have neither a maximum nor a minimumd)none of theseCorrect answer is option 'D'. Can you explain this answer?
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