Question

FInd the equation of the tangent to the curve √x+√y=a at the point (a24,a24)

Answer 1

Integrating y” = 6x one gets

y = x^3 + c1 x + c2 . . . . . . . . . . (1) where c1 and c2 are constants TBD.

Differentiating once

dy/dx = 3x^2 + c1 = 1 at (1,3). So

c1 = 1 - 3 = -2 and substituting for c1 in (1)we write

y = x^3 -2x + c2 . . . . . . . . . . . (2)

Since (1,3) is a point on the curve we can write (2) as

3 = 1 - 2 + c2 . . . . . . . . . . . . . . (3) Hence

c2 = 2 . . . . . . . . . . . . . . . . . . . . .(4) and

substituting for c2 in (2) we get the final equation as

y = x^3 - 2x + 4 . . . . . . . . . . . . .(5)

Mark it as the Brailiest answer ❤