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The minimum value of y=5x^(2)-2x+1 is...

The minimum value of `y=5x^(2)-2x+1` is

A

`(1)/(5)`

B

`(2)/(5)`

C

`(4)/(5)`

D

`(3)/(5)`

Text Solution

Verified by Experts

The correct Answer is:
3
For maximum/minimum value `(dy)/(dx) = 0 rArr 5(2x) - 2(1)+0 =0 rArr x= (1)/(5)`. Now at `x= (1)/(5), (d^(2)y)/(dx^(2)) =10` which is positive so y has minimum value at `x= (1)/(5)`. Therefore `y_(min)= 5((1)/(5))^(2) - 2((1)/(5))^(2) + 1= (4)/(5)`
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