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Consider the function 3x4 +20x3 −36x2 +44 in the interval [−5,10] , function is maximum at
- a)1
- b)0
- c)2
- d)3
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Consider the function 3x4 +20x3 −36x2 +44 in the interval [&minu...
Let f(x) = 3x4 + 20x3 – 36x2 + 44
f '(x) = 12x3 + 60x2 – 72x
f'(x) = 0
12x3 + 60x2 – 72x = 0
12x (x2 + 5x – 6) = 0
12x (x – 3) (x – 2) = 0
x = 0, 2, 3
f''(x) = 36x2 + 120x – 72
f''(0) = –72 < 0
f''(2) = 312 > 0
f''(3) = 612 > 0
∴ function has a maxima at x = 0
f '(x) = 12x3 + 60x2 – 72x
f'(x) = 0
12x3 + 60x2 – 72x = 0
12x (x2 + 5x – 6) = 0
12x (x – 3) (x – 2) = 0
x = 0, 2, 3
f''(x) = 36x2 + 120x – 72
f''(0) = –72 < 0
f''(2) = 312 > 0
f''(3) = 612 > 0
∴ function has a maxima at x = 0
Most Upvoted Answer
Consider the function 3x4 +20x3 −36x2 +44 in the interval [&minu...
Let f(x) = 3x4 + 20x3 – 36x2 + 44
f '(x) = 12x3 + 60x2 – 72x
f'(x) = 0
12x3 + 60x2 – 72x = 0
12x (x2 + 5x – 6) = 0
12x (x – 3) (x – 2) = 0
x = 0, 2, 3
f''(x) = 36x2 + 120x – 72
f''(0) = –72 < 0
f''(2) = 312 > 0
f''(3) = 612 > 0
∴ function has a maxima at x = 0
f '(x) = 12x3 + 60x2 – 72x
f'(x) = 0
12x3 + 60x2 – 72x = 0
12x (x2 + 5x – 6) = 0
12x (x – 3) (x – 2) = 0
x = 0, 2, 3
f''(x) = 36x2 + 120x – 72
f''(0) = –72 < 0
f''(2) = 312 > 0
f''(3) = 612 > 0
∴ function has a maxima at x = 0
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Community Answer
Consider the function 3x4 +20x3 −36x2 +44 in the interval [&minu...
The function you provided, 3x^4 - 20x^3, is a polynomial function of degree 4. It is a fourth-degree polynomial function.
Polynomial functions are functions that are expressed as the sum of terms, where each term consists of a coefficient multiplied by a variable raised to a non-negative integer power. In this case, the function has two terms: 3x^4 and -20x^3.
The highest power of x in the function is 4, so the degree of the polynomial is 4. The degree of a polynomial is the highest power of the variable in the function.
Polynomial functions of degree 4 are known as quartic functions. They can have various shapes and characteristics depending on the coefficients of the terms. The specific shape and behavior of the function can be determined by analyzing its graph or by using calculus techniques such as finding its critical points, intervals of increase/decrease, and concavity.
Without further information about the context or the purpose of the function, it is not possible to provide more specific details about its properties.
Polynomial functions are functions that are expressed as the sum of terms, where each term consists of a coefficient multiplied by a variable raised to a non-negative integer power. In this case, the function has two terms: 3x^4 and -20x^3.
The highest power of x in the function is 4, so the degree of the polynomial is 4. The degree of a polynomial is the highest power of the variable in the function.
Polynomial functions of degree 4 are known as quartic functions. They can have various shapes and characteristics depending on the coefficients of the terms. The specific shape and behavior of the function can be determined by analyzing its graph or by using calculus techniques such as finding its critical points, intervals of increase/decrease, and concavity.
Without further information about the context or the purpose of the function, it is not possible to provide more specific details about its properties.
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Consider the function 3x4 +20x3 −36x2 +44 in the interval [−5,10] , function is maximum ata)1b)0c)2d)3Correct answer is option 'B'. Can you explain this answer?
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Consider the function 3x4 +20x3 −36x2 +44 in the interval [−5,10] , function is maximum ata)1b)0c)2d)3Correct answer is option 'B'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Consider the function 3x4 +20x3 −36x2 +44 in the interval [−5,10] , function is maximum ata)1b)0c)2d)3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the function 3x4 +20x3 −36x2 +44 in the interval [−5,10] , function is maximum ata)1b)0c)2d)3Correct answer is option 'B'. Can you explain this answer?.
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