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Let f(x) is a five degree polynomial which has critical points x = ±1 and  = 4 then which one is incorrect.  
  • a)
    f(x) has minima at x = 1 & maxima at x =  –1 
  • b)
    f(1) –4f(–1) = 4 
  • c)
    f(x) is maxima at x = 1 and minima at x = –1 
  • d)
    f(x) is odd 
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Let f(x) is a five degree polynomial which has critical points x =&plu...
f(x) = ax5  +bx4 + cx3
= 4
⇒ 2 + c = 4
⇒ c = 2
f'(x) = 5ax4  + 4bx3 + 6x2

f'(1) = 0  ⇒  5a + 4b + 6 = 0
f'(–1) = 0  ⇒ 5a – 4b + 6 = 0
b = 0,


f'(x) = –6x4 + 6x2
= 6x2 (–x2 +1)
= –6x2 (x+1) (x–1)

Minimal at x = –1
Maxima at x = 1
x = –1
x = 1
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Let f(x) is a five degree polynomial which has critical points x =&plu...
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Community Answer
Let f(x) is a five degree polynomial which has critical points x =&plu...
f(x) = ax5  +bx4 + cx3
= 4
⇒ 2 + c = 4
⇒ c = 2
f'(x) = 5ax4  + 4bx3 + 6x2

f'(1) = 0  ⇒  5a + 4b + 6 = 0
f'(–1) = 0  ⇒ 5a – 4b + 6 = 0
b = 0,


f'(x) = –6x4 + 6x2
= 6x2 (–x2 +1)
= –6x2 (x+1) (x–1)

Minimal at x = –1
Maxima at x = 1
x = –1
x = 1
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Let f(x) is a five degree polynomial which has critical points x =±1and= 4then which oneis incorrect.a)f(x) has minima at x = 1 & maxima at x = –1b)f(1) –4f(–1) = 4c)f(x) is maxima at x = 1 and minima at x = –1d)f(x) is oddCorrect answer is option 'A'. Can you explain this answer?
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Let f(x) is a five degree polynomial which has critical points x =±1and= 4then which oneis incorrect.a)f(x) has minima at x = 1 & maxima at x = –1b)f(1) –4f(–1) = 4c)f(x) is maxima at x = 1 and minima at x = –1d)f(x) is oddCorrect answer is option 'A'. 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) is a five degree polynomial which has critical points x =±1and= 4then which oneis incorrect.a)f(x) has minima at x = 1 & maxima at x = –1b)f(1) –4f(–1) = 4c)f(x) is maxima at x = 1 and minima at x = –1d)f(x) is oddCorrect answer is option 'A'. 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) is a five degree polynomial which has critical points x =±1and= 4then which oneis incorrect.a)f(x) has minima at x = 1 & maxima at x = –1b)f(1) –4f(–1) = 4c)f(x) is maxima at x = 1 and minima at x = –1d)f(x) is oddCorrect answer is option 'A'. Can you explain this answer?.
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