Continuity And Differentiability

Question

The equation of the tangent to the curve $straight y equals straight x space plus space 4 over straight x squared$ , that is parallel to the x-axis, is

y = 0

y = 1

y = 3

y =2

Solution

y = 3

space straight y space equals space straight x space plus space 4 over straight x squared

On differentiating w.r.t, we get
dy/dx = 1-8/x³

since the tangent is parallel to X-axis, therefore
⇒ x³ = 8
⇒ x = 2 and y = 3