Help with calculus multiple choice?

Question

Would appreciate answer and working out, thank you

Answer 1

Ans. A

Explanation:

y=f(x)

=>

y'=f '(x)=-1/(2x)

[the slope of a curve at

(x,y) is the -ve reciprocal

of that of its normal at the

same point].

Answer 2

The normal to the curve will be the negative inverse of the tangent to the curve

(dy/dx) * (2x) = -1

dy/dx = -1/(2x)

y = (-1/2) * ln|x| + C