Calculus Question.Please help!!

Question

Given the equation y^2=x. which of the following is correct. justify your answer.

a) y is a function of x

b) for every x, y=squarerootx

c) y is not differentiable at x=0

d) the tangent line to the graph of the equation at (0,0) is horizontal.

e)none of the above

Answer 1

y^2 = x

Differentiate both sides with respect to x,

2yy' = 1

y' = 1/(2y)

At x = 0, y = 0. Therefore, y' is undefined.

 

Answer: c