JEE Exam > JEE Questions > Let f(x) = x3 + 3x2 + 3x + 2. Then, at x = -1...
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Let f(x) = x3 + 3x2 + 3x + 2. Then, at x = -1
- a)f(x) has a maximum
- b)f(x) has a minimum
- c)f'(x) has a maximum
- d)f'(x) has a minimum
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Let f(x) = x3 + 3x2 + 3x + 2. Then, at x = -1a)f(x) has a maximumb)f(x...
f(x) = (x+1)3 + 1 ∴ f'(x) = 3(x+1)2.
f'(x) = 0 ⇒ x = -1.
Now, f" (-1 - ∈) = 3(-∈)2 > 0, f'(-1 + ∈)2 = 3∈2 > 0.
∴ f(x) has neither a maximum nor a minimum at x = -1.
Let f'(x) = φ ′ (x) = 3(x+1)2 ∴ φ ′ (x) = 6(x+1).
φ ′ (x) = 0 ⇒ x = -1
φ ′ (-1-∈) = 6(-∈) < 0, φ ′ (-1-∈) = 6∈ > 0
∴ φ (x) has a minimum at x = -1
f'(x) = 0 ⇒ x = -1.
Now, f" (-1 - ∈) = 3(-∈)2 > 0, f'(-1 + ∈)2 = 3∈2 > 0.
∴ f(x) has neither a maximum nor a minimum at x = -1.
Let f'(x) = φ ′ (x) = 3(x+1)2 ∴ φ ′ (x) = 6(x+1).
φ ′ (x) = 0 ⇒ x = -1
φ ′ (-1-∈) = 6(-∈) < 0, φ ′ (-1-∈) = 6∈ > 0
∴ φ (x) has a minimum at x = -1
Most Upvoted Answer
Let f(x) = x3 + 3x2 + 3x + 2. Then, at x = -1a)f(x) has a maximumb)f(x...
Solution:
To find whether f(x) has a maximum or minimum at x = -1, we need to calculate the derivative of f(x) and evaluate it at x = -1.
Differentiating f(x) with respect to x, we get:
f'(x) = 3x2 - 6x + 3
Evaluating f'(x) at x = -1, we get:
f'(-1) = 3(-1)2 - 6(-1) + 3 = 12
Since f'(-1) is positive, f(x) has a minimum at x = -1.
Therefore, the correct answer is option 'D'.
Explanation:
When the derivative of a function is positive at a point, it indicates that the function is increasing at that point. Similarly, when the derivative is negative, it indicates that the function is decreasing at that point. If the derivative changes sign from positive to negative, the function has a maximum at that point, and if the derivative changes sign from negative to positive, the function has a minimum at that point.
In this case, we have calculated the derivative of f(x) and evaluated it at x = -1. Since the derivative is positive at x = -1, it indicates that f(x) is increasing at x = -1. Therefore, f(x) has a minimum at x = -1.
To find whether f(x) has a maximum or minimum at x = -1, we need to calculate the derivative of f(x) and evaluate it at x = -1.
Differentiating f(x) with respect to x, we get:
f'(x) = 3x2 - 6x + 3
Evaluating f'(x) at x = -1, we get:
f'(-1) = 3(-1)2 - 6(-1) + 3 = 12
Since f'(-1) is positive, f(x) has a minimum at x = -1.
Therefore, the correct answer is option 'D'.
Explanation:
When the derivative of a function is positive at a point, it indicates that the function is increasing at that point. Similarly, when the derivative is negative, it indicates that the function is decreasing at that point. If the derivative changes sign from positive to negative, the function has a maximum at that point, and if the derivative changes sign from negative to positive, the function has a minimum at that point.
In this case, we have calculated the derivative of f(x) and evaluated it at x = -1. Since the derivative is positive at x = -1, it indicates that f(x) is increasing at x = -1. Therefore, f(x) has a minimum at x = -1.
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Let f(x) = x3 + 3x2 + 3x + 2. Then, at x = -1a)f(x) has a maximumb)f(x) has a minimumc)f(x) has a maximumd)f(x) has a minimumCorrect answer is option 'D'. Can you explain this answer?
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Let f(x) = x3 + 3x2 + 3x + 2. Then, at x = -1a)f(x) has a maximumb)f(x) has a minimumc)f(x) has a maximumd)f(x) has a minimumCorrect answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let f(x) = x3 + 3x2 + 3x + 2. Then, at x = -1a)f(x) has a maximumb)f(x) has a minimumc)f(x) has a maximumd)f(x) has a minimumCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let f(x) = x3 + 3x2 + 3x + 2. Then, at x = -1a)f(x) has a maximumb)f(x) has a minimumc)f(x) has a maximumd)f(x) has a minimumCorrect answer is option 'D'. Can you explain this answer?.
Let f(x) = x3 + 3x2 + 3x + 2. Then, at x = -1a)f(x) has a maximumb)f(x) has a minimumc)f(x) has a maximumd)f(x) has a minimumCorrect answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let f(x) = x3 + 3x2 + 3x + 2. Then, at x = -1a)f(x) has a maximumb)f(x) has a minimumc)f(x) has a maximumd)f(x) has a minimumCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let f(x) = x3 + 3x2 + 3x + 2. Then, at x = -1a)f(x) has a maximumb)f(x) has a minimumc)f(x) has a maximumd)f(x) has a minimumCorrect answer is option 'D'. Can you explain this answer?.
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