Question

The minimum value of $2a^2-3a+10$ is

• A. $\frac{15}{2}$
• B. $\frac{11}{2}$
• C. $-\frac{13}{2}$
• D. $\frac{71}{8}$

Answer 1

The correct option is D

$\frac{71}{8}$

Find the minimum value of the given function

Given : $f\left(a\right)=2a^2-3a+10$

Differentiate with respect to $a$,

$$\begin{gathered} f\text{'}\left(a\right)=2\left(2\right)a-3\left[\frac{d}{dx}{x}^n=n.x^{n-1}\right] \\ \Rightarrow f\text{'}\left(a\right)=4a-3 \end{gathered}$$

To find the minimum value $f\text{'}\left(a\right)=0$

$$\begin{gathered} \Rightarrow 4a-3=0 \\ \Rightarrow a=\frac{3}{4} \end{gathered}$$

Now, evaluate the minimum value of the function

$$\begin{gathered} f{\left(a\right)}_{min}=2{\left(\frac{3}{4}\right)}^2-3\left(\frac{3}{4}\right)+10 \\ \Rightarrow f{\left(a\right)}_{min}=\frac{9}{8}-\frac{9}{4}+10 \\ \Rightarrow f{\left(a\right)}_{min}=\frac{71}{8} \end{gathered}$$

Hence option $\left(D\right)$ is the correct option.