CPM Homework Help : APCALC Problem 8-128

Multiple Choice: If $x^2 + y^2 = 25$ then $\frac { d ^ { 2 } y } { d x ^ { 2 } }=$

$- \frac { x } { y }$

$\frac { x + y } { y ^ { 2 } }$

$- \frac { 25 } { y ^ { 3 } }$

$\frac { x ^ { 2 } - y ^ { 2 } } { y ^ { 3 } }$

$\frac { y ^ { 2 } - x } { y ^ { 3 } }$

Step 1:

$\frac{d}{dx}(x^{2}+y^{2})=\frac{d}{dx}25$

$\frac{dy}{dx}=\frac{-x}{y}$

Step 2:

$\frac{d^{2}y}{dx^{2}}=\frac{d}{dx}\left (\frac{-x}{y} \right )$

$\frac{d^{2}y}{dx^{2}}=\frac{-(y^{2}+x^{2})}{y^{3}}$

Answer:

Uh-oh! None of the multiple choice options match! That does not mean you are wrong. Look at the original equation of the circle.
What does $x^2 + y^2$ equal? Substitute that value and find your solution.