Question

a curve is defined for x>0 and in such that dy/dx=x+(4)/(x^2) the point P(4,8) lies on the curve

(i) show the equation of the curve
(ii) show that the gradient of the curve has a minimum value when x=2 and state this minimum value.

Answer 1

By integration:

Answer 2

Y={xdx +4{x^-2 dx

Answer 3

=x^2/2-4/x+c base 0

Answer 4

Let (c): curve

Answer 5

P€(c) : y(4)=8

Answer 6

That is 4^2/2-4/4+c base 0=8

Answer 7

→ c base 0 =1

Answer 8

Y=x^2/2 - 4/x +1