The function f defined by f(x) = x3 $$-$$ 3x2 + 5x + 7 , is :
JEE · Math · previous-year question
- A.increasing in R.correct
- B.decreasing in R.
- C.decreasing in (0, $$\infty $$) and increasing in ($$-$$ $$\infty $$, 0)
- D.increasing in (0, $$\infty $$) and decreasing in ($$-$$ $$\infty $$, 0)
Answer
A. increasing in R.
Explanation
The given function is $$f(x) = {x^2} - 3{x^2} + 5x + 7$$ $$f'(x) = 3{x^2} - 6x + 5$$ The discriminant of the above quadratic equation is $$\Delta = 36 - 4(3)(5) = 36 - 60 Therefore, $$f'(x) > 0 \forall x \in {R^ + }$$ Also, $$f'(x) > 0 \forall x \in {R^ - }$$ Therefore, the given function f is increasing in R.
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