Question

Find the minimum value of the function $y=5x^2-2x+1$.

• A. $0.4$
• B. $0.8$
• C. $1.2$
• D. $1.6$

Answer 1

The correct option is B $0.8$

For finding minimum value, we will first find critical points.
$\frac{dy}{dx}=0$
$\Rightarrow \frac{dy}{dx}=10x-2=0$
$\Rightarrow 10x=2$
$\Rightarrow x=\frac{1}{5}$
Further, $\frac{d^{2}y}{d{x}^2}=10$
Since $\frac{d^{2}y}{d^{2}x}$ is positive for all values, $y_{(x=\frac{1}{5})}$ is minimum value.
$\Rightarrow y_{(x=\frac{1}{5})}=5{\left(\frac{1}{5}\right)}^2-2\left(\frac{1}{5}\right)+1$
$=\frac{1}{5}-\frac{2}{5}+\frac{5}{5}=\frac{4}{5}=0.8$