Question

1. If y depends on X according to relation
- y = 25x2 – 10x + 10, then minimum value of y will
be​

Answer 1

it is given that, y = 25x² - 10x + 10

we have to find minimum value of y,

differentiating y with respect to x,

dy/dx = d(25x² - 10x + 10)/dx

= d(25x²)/dx - d(10x)/dx + d(10)/dx

= 25 × d(x²)/dx - 10 × dx/dx + 0

= 25 × 2x - 10

= 50x - 10

now, find value of x at dy/dx = 0

so, 50x - 10 = 0 => x = 1/5

again differentiating with respect to x,

d²y/dx² = 50 > 0 for real value of x.

so, at x = 1/5 , y will be minimum.

so, minimum value of y = 25(1/5)² - 10(1/5) + 10

= 1 - 2 + 10 = 9

hence, minimum value of y = 9