Let &fnof;(x) be non-constant thrice differentiable function defined on (–∞, ∞) such that&fnof;(x) = &fnof;(6 – x) and &fnof;(0) = 0 = &fnof;(2) = &fnof;(5).If n is the minimum number of roots of (&fnof;"(x))2+ &fnof;(x)&fnof;"(x) = 0 in the intervalx ∈ [0, 6] then sum of digits of n equalsCorrect answer is '3'. Can you explain this answer?

Let andfnof;(x) be non-constant thrice differentiable function defined on (andndash;andinfin;, andinfin;) such thatandfnof;(x) = andfnof;(6 andndash; x) and andfnof;(0) = 0 = andfnof;(2) = andfnof;(5).If n is the minimum number of roots of (andfnof;andquot;(x))2+ andfnof;(x)andfnof;andquot;(x) = 0 in the intervalx andisin; [0, 6] then sum of digits of n equalsCorrect answer is '3'. Can you explain this answer?

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Let ƒ(x) be non-constant thrice differentiable function defined on (–∞, ∞) such that ƒ(x) = ƒ(6 – x) and ƒ'(0) = 0 = ƒ'(2) = ƒ'(5). If 'n' is the minimum number of roots of (ƒ"(x))² + ƒ'(x)ƒ"'(x) = 0 in the interval x ∈ [0, 6] then sum of digits of n equals

Correct answer is '3'. Can you explain this answer?

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Let ƒ(x) be non-constant thrice differentiable function defined o...

ƒ(x) = ƒ(6 – x)
⇒ ƒ'(x) = –ƒ'(6 – x) .... (1)
put x = 0, 2, 5
ƒ'(0) = ƒ'(6) = ƒ'(2) = ƒ'(4) = ƒ'(5) = ƒ'(1) = 0
and from equation (1) we get ƒ'(3) = –ƒ'(3)
⇒ ƒ'(3) = 0
So ƒ'(x) = 0 has minimum 7 roots in
x ∈ [0, 6] ⇒ ƒ"(x) has min 6 roots in x ∈ [0,6]
h(x) = ƒ'(x).ƒ"(x)
h'(x) = (ƒ"(x))² + ƒ'(x) ƒ"'(x)
h(x) = 0 has 13 roots in x ∈ [0, 6]
h'(x) = 0 has 12 roots in x ∈ [0, 6]

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Let ƒ(x) be non-constant thrice differentiable function defined on (–∞, ∞) such thatƒ(x) = ƒ(6 – x) and ƒ(0) = 0 = ƒ(2) = ƒ(5).If n is the minimum number of roots of (ƒ"(x))2+ ƒ(x)ƒ"(x) = 0 in the intervalx ∈ [0, 6] then sum of digits of n equalsCorrect answer is '3'. Can you explain this answer?

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Let ƒ(x) be non-constant thrice differentiable function defined on (–∞, ∞) such thatƒ(x) = ƒ(6 – x) and ƒ(0) = 0 = ƒ(2) = ƒ(5).If n is the minimum number of roots of (ƒ"(x))2+ ƒ(x)ƒ"(x) = 0 in the intervalx ∈ [0, 6] then sum of digits of n equalsCorrect 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 ƒ(x) be non-constant thrice differentiable function defined on (–∞, ∞) such thatƒ(x) = ƒ(6 – x) and ƒ(0) = 0 = ƒ(2) = ƒ(5).If n is the minimum number of roots of (ƒ"(x))2+ ƒ(x)ƒ"(x) = 0 in the intervalx ∈ [0, 6] then sum of digits of n equalsCorrect 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 ƒ(x) be non-constant thrice differentiable function defined on (–∞, ∞) such thatƒ(x) = ƒ(6 – x) and ƒ(0) = 0 = ƒ(2) = ƒ(5).If n is the minimum number of roots of (ƒ"(x))2+ ƒ(x)ƒ"(x) = 0 in the intervalx ∈ [0, 6] then sum of digits of n equalsCorrect answer is '3'. Can you explain this answer?.

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