매개변수 접선 기울기

$\displaystyle x = t ^{3} , \frac{dx}{dt} = 3 t ^{2} , x = 8$일 때, $t = 2$ $\displaystyle y = 2 t - \sqrt{2 t} , \frac{dy}{dt} = t - \frac{1}{\sqrt{2 t}} , t = 2$일 때, $a = 2$ $\displaystyle \frac{dy}{dx} | _{x = 8} = \frac{\frac{dy}{dt} | _{t = 2}}{\frac{dx}{dt} | _{t = 2}} = \frac{\left[ t - \frac{1}{\sqrt{2 t}} \right] _{t = 2}}{\left[ 3 t ^{2} \right] _{t = 2}} = \frac{1}{8} = b$ $\displaystyle \therefore 100 ab = 100 \cdot 2 \cdot \frac{1}{8} = 25$