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Let f(x) be a polynomial of degree 5 such that x = ±1 are its critical points. If 
, then which one of the following is not true?
, then which one of the following is not true?- a)f is an odd function.
- b)x = 1 is a point of minima and x = -1 is a point of maxima of f.
- c)f(1) - 4f(-1) = 4
- d)x = 1 is a point of maxima and x = -1 is a point of minimum of f.
Correct answer is option 'B'. Can you explain this answer?
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Let f(x) be a polynomial of degree 5 such that x =±1are its cri...
∵ f(x) is a five-degree polynomial such that 
Let f(x) = ax5 + bx4 + cx
⇒ 2 + c = 4
⇒ c = 2.
Now, f'(x) = 5ax4 + 4bx3 + 3cx2
= x2(5ax2 + 4bx + 3c)
f'(1) = 0
⇒ 5a + 4b + 6 = 0
And f'(-1) = 0
∴ 5a - 4b + 6 = 0
∴ b = 0, a = -6/5
∴ f(x) = - 6/5x5 + 2x3
f'(x) = -6x4 + 6x2 = -6x2(x + 1) (x - 1)
It is clear that maximum is at x = 1 and minimum is at x = -1.
And f(1) - 4f(-1) = 4
Let f(x) = ax5 + bx4 + cx
⇒ 2 + c = 4
⇒ c = 2.
Now, f'(x) = 5ax4 + 4bx3 + 3cx2
= x2(5ax2 + 4bx + 3c)
f'(1) = 0
⇒ 5a + 4b + 6 = 0
And f'(-1) = 0
∴ 5a - 4b + 6 = 0
∴ b = 0, a = -6/5
∴ f(x) = - 6/5x5 + 2x3
f'(x) = -6x4 + 6x2 = -6x2(x + 1) (x - 1)
It is clear that maximum is at x = 1 and minimum is at x = -1.
And f(1) - 4f(-1) = 4
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Let f(x) be a polynomial of degree 5 such that x =±1are its critical points. If , then which one of the following is not true?a)f is an odd function.b)x = 1 is a point of minima and x = -1 is a point of maxima of f.c)f(1) - 4f(-1) = 4d)x = 1 is a point of maxima and x = -1 is a point of minimum of f.Correct answer is option 'B'. Can you explain this answer?
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Let f(x) be a polynomial of degree 5 such that x =±1are its critical points. If , then which one of the following is not true?a)f is an odd function.b)x = 1 is a point of minima and x = -1 is a point of maxima of f.c)f(1) - 4f(-1) = 4d)x = 1 is a point of maxima and x = -1 is a point of minimum of f.Correct answer is option 'B'. 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) be a polynomial of degree 5 such that x =±1are its critical points. If , then which one of the following is not true?a)f is an odd function.b)x = 1 is a point of minima and x = -1 is a point of maxima of f.c)f(1) - 4f(-1) = 4d)x = 1 is a point of maxima and x = -1 is a point of minimum of f.Correct answer is option 'B'. 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) be a polynomial of degree 5 such that x =±1are its critical points. If , then which one of the following is not true?a)f is an odd function.b)x = 1 is a point of minima and x = -1 is a point of maxima of f.c)f(1) - 4f(-1) = 4d)x = 1 is a point of maxima and x = -1 is a point of minimum of f.Correct answer is option 'B'. Can you explain this answer?.
Let f(x) be a polynomial of degree 5 such that x =±1are its critical points. If , then which one of the following is not true?a)f is an odd function.b)x = 1 is a point of minima and x = -1 is a point of maxima of f.c)f(1) - 4f(-1) = 4d)x = 1 is a point of maxima and x = -1 is a point of minimum of f.Correct answer is option 'B'. 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) be a polynomial of degree 5 such that x =±1are its critical points. If , then which one of the following is not true?a)f is an odd function.b)x = 1 is a point of minima and x = -1 is a point of maxima of f.c)f(1) - 4f(-1) = 4d)x = 1 is a point of maxima and x = -1 is a point of minimum of f.Correct answer is option 'B'. 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) be a polynomial of degree 5 such that x =±1are its critical points. If , then which one of the following is not true?a)f is an odd function.b)x = 1 is a point of minima and x = -1 is a point of maxima of f.c)f(1) - 4f(-1) = 4d)x = 1 is a point of maxima and x = -1 is a point of minimum of f.Correct answer is option 'B'. Can you explain this answer?.
Solutions for Let f(x) be a polynomial of degree 5 such that x =±1are its critical points. If , then which one of the following is not true?a)f is an odd function.b)x = 1 is a point of minima and x = -1 is a point of maxima of f.c)f(1) - 4f(-1) = 4d)x = 1 is a point of maxima and x = -1 is a point of minimum of f.Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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ample number of questions to practice Let f(x) be a polynomial of degree 5 such that x =±1are its critical points. If , then which one of the following is not true?a)f is an odd function.b)x = 1 is a point of minima and x = -1 is a point of maxima of f.c)f(1) - 4f(-1) = 4d)x = 1 is a point of maxima and x = -1 is a point of minimum of f.Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice JEE tests.
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