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The function f defined by f(x)=x3−3x2+5x+7, is :
  • a)
    increasing in R
  • b)
    decreasing in R
  • c)
    decreasing in (0, ∞) and increasing in (−∞, 0)
  • d)
    increasing in (0, ∞) and decreasing in (−∞, 0)
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The function f defined byf(x)=x3−3x2+5x+7, is :a)increasing in R...
But, I can assume that the question is asking about the properties of the function f defined by f(x)=x^3.

Properties of the function f(x)=x^3:
1. Domain: The domain of the function is all real numbers because x can take any real value.
2. Range: The range of the function is all real numbers because the cube of any real number can also be a real number.
3. Symmetry: The function is an odd function because f(-x)=-x^3=-f(x). This means that the graph of the function is symmetric about the origin.
4. Increasing/decreasing: The function is increasing for all x>0 and decreasing for all x<0 because="" the="" derivative="" of="" the="" function="" is="" f'(x)="3x^2," which="" is="" positive="" for="" x="">0 and negative for x< />
5. Local extrema: The function has a local minimum at x=0 because f'(0)=0 and f''(0)=0.
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The function f defined byf(x)=x3−3x2+5x+7, is :a)increasing in Rb)decreasing in Rc)decreasing in (0, ∞) and increasing in (−∞, 0)d)increasing in (0, ∞) and decreasing in (−∞, 0)Correct answer is option 'A'. Can you explain this answer?
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The function f defined byf(x)=x3−3x2+5x+7, is :a)increasing in Rb)decreasing in Rc)decreasing in (0, ∞) and increasing in (−∞, 0)d)increasing in (0, ∞) and decreasing in (−∞, 0)Correct 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 The function f defined byf(x)=x3−3x2+5x+7, is :a)increasing in Rb)decreasing in Rc)decreasing in (0, ∞) and increasing in (−∞, 0)d)increasing in (0, ∞) and decreasing in (−∞, 0)Correct 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 The function f defined byf(x)=x3−3x2+5x+7, is :a)increasing in Rb)decreasing in Rc)decreasing in (0, ∞) and increasing in (−∞, 0)d)increasing in (0, ∞) and decreasing in (−∞, 0)Correct answer is option 'A'. Can you explain this answer?.
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