Mathematics Exam > Mathematics Questions > Let f(x) = (x – 2)17 (x + 5)24. Thena)f...
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Let f(x) = (x – 2)17 (x + 5)24. Then
- a)f does not have a critical point at 2
- b)f has a minimum at 2
- c)f has neither minimum nor a maximum at x = 2
- d)f has a maximum at 2
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Let f(x) = (x – 2)17 (x + 5)24. Thena)f does not have a critical...
Here f(x) = (x – 2)17 (x + 5)24
f17 (2) ≠ 0
⇒ Odd derivative of function is non-zero. So, f has neither a minimum nor a maximum at 2.
f17 (2) ≠ 0
⇒ Odd derivative of function is non-zero. So, f has neither a minimum nor a maximum at 2.
Most Upvoted Answer
Let f(x) = (x – 2)17 (x + 5)24. Thena)f does not have a critical...
Here f(x) = (x – 2)17 (x + 5)24
f17 (2) ≠ 0
⇒ Odd derivative of function is non-zero. So, f has neither a minimum nor a maximum at 2.
f17 (2) ≠ 0
⇒ Odd derivative of function is non-zero. So, f has neither a minimum nor a maximum at 2.
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Community Answer
Let f(x) = (x – 2)17 (x + 5)24. Thena)f does not have a critical...
Understanding the Function f(x)
The function given is f(x) = (x - 2)^17 * (x + 5)^24. To analyze the behavior of f(x) at x = 2, we need to investigate its critical points and local extrema.
Critical Points
- A critical point occurs where the derivative f'(x) is zero or undefined.
- To find f'(x), we apply the product rule and analyze the behavior near x = 2.
Behavior at x = 2
- At x = 2, the term (x - 2)^17 equals zero, making f(2) = 0.
- The derivative f'(x) will also involve (x - 2) terms, leading to f'(2) = 0.
Local Extrema Analysis
- To determine the nature of the critical point at x = 2, we examine f(x) around this point.
- As x approaches 2 from the left, f(x) is negative (since (x - 2)^17 is negative).
- As x approaches 2 from the right, f(x) is still negative (since (x - 2)^17 is positive).
- Therefore, f(x) does not change sign around x = 2, indicating that it is neither a maximum nor a minimum.
Conclusion
- Since f(x) does not have a change in direction around x = 2, it confirms that:
- f has neither a minimum nor a maximum at x = 2.
Thus, the correct answer is option 'C'.
The function given is f(x) = (x - 2)^17 * (x + 5)^24. To analyze the behavior of f(x) at x = 2, we need to investigate its critical points and local extrema.
Critical Points
- A critical point occurs where the derivative f'(x) is zero or undefined.
- To find f'(x), we apply the product rule and analyze the behavior near x = 2.
Behavior at x = 2
- At x = 2, the term (x - 2)^17 equals zero, making f(2) = 0.
- The derivative f'(x) will also involve (x - 2) terms, leading to f'(2) = 0.
Local Extrema Analysis
- To determine the nature of the critical point at x = 2, we examine f(x) around this point.
- As x approaches 2 from the left, f(x) is negative (since (x - 2)^17 is negative).
- As x approaches 2 from the right, f(x) is still negative (since (x - 2)^17 is positive).
- Therefore, f(x) does not change sign around x = 2, indicating that it is neither a maximum nor a minimum.
Conclusion
- Since f(x) does not have a change in direction around x = 2, it confirms that:
- f has neither a minimum nor a maximum at x = 2.
Thus, the correct answer is option 'C'.
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Let f(x) = (x – 2)17 (x + 5)24. Thena)f does not have a critical point at 2b)f has a minimum at 2c)f has neither minimum nor a maximum at x = 2d)f has a maximum at 2Correct answer is option 'C'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let f(x) = (x – 2)17 (x + 5)24. Thena)f does not have a critical point at 2b)f has a minimum at 2c)f has neither minimum nor a maximum at x = 2d)f has a maximum at 2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let f(x) = (x – 2)17 (x + 5)24. Thena)f does not have a critical point at 2b)f has a minimum at 2c)f has neither minimum nor a maximum at x = 2d)f has a maximum at 2Correct answer is option 'C'. Can you explain this answer?.
Let f(x) = (x – 2)17 (x + 5)24. Thena)f does not have a critical point at 2b)f has a minimum at 2c)f has neither minimum nor a maximum at x = 2d)f has a maximum at 2Correct answer is option 'C'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let f(x) = (x – 2)17 (x + 5)24. Thena)f does not have a critical point at 2b)f has a minimum at 2c)f has neither minimum nor a maximum at x = 2d)f has a maximum at 2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let f(x) = (x – 2)17 (x + 5)24. Thena)f does not have a critical point at 2b)f has a minimum at 2c)f has neither minimum nor a maximum at x = 2d)f has a maximum at 2Correct answer is option 'C'. Can you explain this answer?.
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Let f(x) = (x – 2)17 (x + 5)24. Thena)f does not have a critical point at 2b)f has a minimum at 2c)f has neither minimum nor a maximum at x = 2d)f has a maximum at 2Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Let f(x) = (x – 2)17 (x + 5)24. Thena)f does not have a critical point at 2b)f has a minimum at 2c)f has neither minimum nor a maximum at x = 2d)f has a maximum at 2Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Let f(x) = (x – 2)17 (x + 5)24. Thena)f does not have a critical point at 2b)f has a minimum at 2c)f has neither minimum nor a maximum at x = 2d)f has a maximum at 2Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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