if y'0 and y=1 when x=2 and y''-4=0, find the function

Answer 1

When x = 2, y' = 0 and y = 1.

If y'' - 4 = 0, then y''=4.

Finding an antiderivative:

y' = 4x + C₁

0 = 4(2) + C₁

C₁= -8

y' = 4x - 8

Find the antiderivative for y':

y = 2x² -8x + C₂

1 = 2(2)² - 8(2) + C₂

1 = -8 + C₂

C₂= 9

So, f(x) = 2x² -8x + 9