What is the minimum value of `2x^(2)-3x+5` ?

Options

A. 0
B. `3//4`
C. `31//4`
D. `31//8`

Answer

D

Explanation

Let y `=2x^(2)-3x+5`
`rarr (dy)/(dx)=4x-3`
and `(d^(2)y)/(dx^(2))=4`
For maximum and minimum value of y
`(dy)/(dx)=0`
`rarr 4x-3=0`
`rarr x=3/4`
Since for every value of `x,(d^(2)y)/(dx^(2))` =+ve`
So minimum value of `2x^(2)-3x+5` is minimum `x=3/4`
`therefore` The minimum value =`2((3)/(4))^(2)-3((3)/(4))+5`
`=9/8-9/4+5=(9-18+40)/(8)=(31)/(8)`