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What is the nature of function f(x) = x3 – 3x2 + 4x on R?
- a)Increasing
- b)Decreasing
- c)Constant
- d)Increasing and Decreasing
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
What is the nature of function f(x) = x3 – 3x2 + 4x on R?a)Incre...
f(x) = x3 – 3x2 + 4x
f’(x) = 3x2 – 6x + 4.
f’(x) = 3(x2 – 2x + 1) + 1.
=> 3(x-1)2 + 1>0, in every interval of R. Therefore the function f is increasing on R.
Most Upvoted Answer
What is the nature of function f(x) = x3 – 3x2 + 4x on R?a)Incre...
The function f(x) = x^3 is a cubic function. It is a polynomial function of degree 3. The function describes a curve that starts from negative infinity and goes to positive infinity. It is an odd function because it is symmetric about the origin (f(-x) = -f(x)). As x approaches negative infinity, f(x) also approaches negative infinity, and as x approaches positive infinity, f(x) also approaches positive infinity. The function has a single inflection point at x = 0.
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What is the nature of function f(x) = x3 – 3x2 + 4x on R?a)Increasingb)Decreasingc)Constantd)Increasing and DecreasingCorrect answer is option 'A'. Can you explain this answer?
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