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QJEEM17Maeaa4: JEE Main 2017 Mathematics - Class 12 JEEM17Maeaa4 Solution: The function f defined by f(x) = x 3 3x 2 + 5x + 7 , is :
The function f defined by
f(x) = x3 3x2 + 5x + 7 , is :
f(x) = x3 3x2 + 5x + 7 , is :
Multiple Choice Options
- A increasing in R.
- B decreasing in R.
- C decreasing in (0, ) and increasing in ( , 0)
- D increasing in (0, ) and decreasing in ( , 0)
Step-by-Step Verified Solution
The given function is
The discriminant of the above quadratic equation is
\Delta = 36 - 4(3)(5) = 36 - 60 < 0
Therefore, f'(x) > 0\,\forall x \in {R^ + }
Also, f'(x) > 0\,\forall x \in {R^ - }
Therefore, the given function f is increasing in R.