The function $f$ defined by $f(x) = x^3 - 3x^2 + 5x + 7$ is:

The function $f$ defined by $f(x) = x^3 - 3x^2 + 5x + 7$ is:
  1. Decreasing in $R$
  2. Increasing in $R$
  3. Increasing in $[0, \infty)$ and decreasing in $(-\infty, 0]$
  4. Decreasing in $(0, \infty)$ and increasing in $(-\infty, 0)$

Solution

We have fx=x3-3x2+5x+7

f′x=3x2-6x+5>0      

D=b2-4ac=36-4·3·5=-14 -ve

Then, f'x>0. 

Hence, fx is increasing in R. 

Asked in: JEE Main 2017 (09 Apr Online)

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