Question

The function $f$ defined by $f(x)=4x^4-2x+1$ is increasing for

• A. $x<1$
• B. $x>0$
• C. $x<\frac{1}{2}$
• D. $x>\frac{1}{2}$

Answer 1

Answer: (D)

We have, $f(x)=4x^4-2x+1$
$\Rightarrow f^{\prime }\left(x\right)=16x^3-2$
The function is increasing if $f^{\prime }\left(x\right)>0$
$\Rightarrow 16x^3-2>0$
$\Rightarrow x>\frac{1}{2}$