Question

The set of values of x for which $f\left(x\right)=x^3+6x^2+24x-17$ is increasing is

• A. $(-\infty ,\infty )$
• B. $R-\left\{O\right\}$
• C. (1, 2)
• D. [1, 2]

Answer 1

The correct option is A $(-\infty ,\infty )$

$f\left(x\right)=x^3+6x^2+24x-17$

$f^{\prime }\left(x\right)=3x^2+12x+24$

$f^{\prime }\left(x\right)=3(x^2+4x)+24$

$f^{\prime }\left(x\right)=3(x^2+4x+4)+24+12$

$f^{\prime }\left(x\right)=3(x+2{)}^2+36>0$

$\text{So,}f\left(x\right)\text{is always increasing}$

$\text{in}(-\infty ,\infty )$