JEE Exam > JEE Questions > Let f(x) = |(x - 1)(x2 - 2x - 3) | + x - 3, x...
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Let f(x) = |(x - 1)(x2 - 2x - 3) | + x - 3, x ∈ R. If m and M are respectively the number of points of local minimum and local maximum of f in the interval (0, 4), then m + M is equal to
Correct answer is '3'. Can you explain this answer?
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Let f(x) = |(x - 1)(x2 - 2x - 3) | + x - 3, x∈ R. If m and M are ...
To find the zeros of the function f(x), we need to find the values of x where f(x) equals zero.
First, let's simplify f(x):
f(x) = |(x - 1)(x^2 - 2x - 3)| * (x - 3)
Now, let's solve for the zeros:
1. (x - 1)(x^2 - 2x - 3) = 0
From this equation, we have two cases:
Case 1: (x - 1) = 0
Solving for x, we get x = 1.
Case 2: (x^2 - 2x - 3) = 0
Using the quadratic formula, we have:
x = (-(-2) ± √((-2)^2 - 4(1)(-3))) / (2(1))
x = (2 ± √(4 + 12)) / 2
x = (2 ± √16) / 2
x = (2 ± 4) / 2
Simplifying further, we get:
x = (2 + 4) / 2 = 6 / 2 = 3
x = (2 - 4) / 2 = -2 / 2 = -1
Therefore, the zeros of the function f(x) are x = 1, x = 3, and x = -1.
First, let's simplify f(x):
f(x) = |(x - 1)(x^2 - 2x - 3)| * (x - 3)
Now, let's solve for the zeros:
1. (x - 1)(x^2 - 2x - 3) = 0
From this equation, we have two cases:
Case 1: (x - 1) = 0
Solving for x, we get x = 1.
Case 2: (x^2 - 2x - 3) = 0
Using the quadratic formula, we have:
x = (-(-2) ± √((-2)^2 - 4(1)(-3))) / (2(1))
x = (2 ± √(4 + 12)) / 2
x = (2 ± √16) / 2
x = (2 ± 4) / 2
Simplifying further, we get:
x = (2 + 4) / 2 = 6 / 2 = 3
x = (2 - 4) / 2 = -2 / 2 = -1
Therefore, the zeros of the function f(x) are x = 1, x = 3, and x = -1.
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Let f(x) = |(x - 1)(x2 - 2x - 3) | + x - 3, x∈ R. If m and M are ...
f(x) = |(x - 1)(x + 1)(x - 3)| + (x - 3)
f'(3+) > 0 f'(3-) < 0 → Minimum
f'(1+) > 0 f'(1-) < 0 → Minimum
x ∈ (1, 3) f'(x) = 0 at one point → Maximum
x ∈ (3, 4) f'(x) ≠ 0
x ∈ (0, 1) f'(x) ≠ 0
So, there are 2 points of minima and 1 point of maxima.
Hence, m + M = 3
f'(3+) > 0 f'(3-) < 0 → Minimum
f'(1+) > 0 f'(1-) < 0 → Minimum
x ∈ (1, 3) f'(x) = 0 at one point → Maximum
x ∈ (3, 4) f'(x) ≠ 0
x ∈ (0, 1) f'(x) ≠ 0
So, there are 2 points of minima and 1 point of maxima.
Hence, m + M = 3
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Let f(x) = |(x - 1)(x2 - 2x - 3) | + x - 3, x∈ R. If m and M are respectively the number of points of local minimum and local maximum of f in the interval (0, 4), then m + M is equal toCorrect answer is '3'. Can you explain this answer?
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Let f(x) = |(x - 1)(x2 - 2x - 3) | + x - 3, x∈ R. If m and M are respectively the number of points of local minimum and local maximum of f in the interval (0, 4), then m + M is equal toCorrect answer is '3'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let f(x) = |(x - 1)(x2 - 2x - 3) | + x - 3, x∈ R. If m and M are respectively the number of points of local minimum and local maximum of f in the interval (0, 4), then m + M is equal toCorrect answer is '3'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let f(x) = |(x - 1)(x2 - 2x - 3) | + x - 3, x∈ R. If m and M are respectively the number of points of local minimum and local maximum of f in the interval (0, 4), then m + M is equal toCorrect answer is '3'. Can you explain this answer?.
Let f(x) = |(x - 1)(x2 - 2x - 3) | + x - 3, x∈ R. If m and M are respectively the number of points of local minimum and local maximum of f in the interval (0, 4), then m + M is equal toCorrect answer is '3'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let f(x) = |(x - 1)(x2 - 2x - 3) | + x - 3, x∈ R. If m and M are respectively the number of points of local minimum and local maximum of f in the interval (0, 4), then m + M is equal toCorrect answer is '3'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let f(x) = |(x - 1)(x2 - 2x - 3) | + x - 3, x∈ R. If m and M are respectively the number of points of local minimum and local maximum of f in the interval (0, 4), then m + M is equal toCorrect answer is '3'. Can you explain this answer?.
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Let f(x) = |(x - 1)(x2 - 2x - 3) | + x - 3, x∈ R. If m and M are respectively the number of points of local minimum and local maximum of f in the interval (0, 4), then m + M is equal toCorrect answer is '3'. Can you explain this answer?, a detailed solution for Let f(x) = |(x - 1)(x2 - 2x - 3) | + x - 3, x∈ R. If m and M are respectively the number of points of local minimum and local maximum of f in the interval (0, 4), then m + M is equal toCorrect answer is '3'. Can you explain this answer? has been provided alongside types of Let f(x) = |(x - 1)(x2 - 2x - 3) | + x - 3, x∈ R. If m and M are respectively the number of points of local minimum and local maximum of f in the interval (0, 4), then m + M is equal toCorrect answer is '3'. Can you explain this answer? theory, EduRev gives you an
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