Mathematics

Problem

Consider the circle

x^{2}+y^{2}=25

. a. (i) Determine

\dfrac{dy}{dx}

in terms of

x

and

y

. b. (ii) Hence find

\dfrac{d^{2}y}{dx^{2}}

in terms of

x

and

y

. c. (iii) Evaluate

\dfrac{d^{2}y}{dx^{2}}

at the point

(3,4)

on the circle.