Cards In This Deck

• $$\begin{gathered} \text{You are asked to find the equation of the Normal to a curve at }x=2\text{.} \\ \text{You have calculated the derivative }\frac{dy}{dx}\text{ and found that at }x=2\text{, the gradient of the curve is }4\text{.} \\ \text{What value do you use for }m\text{ in your line equation }y-y_1=m(x-x_1)\text{?} \end{gathered}$$
  $$\begin{gathered} m=-\frac{1}{4} \\ \text{(The negative reciprocal)} \end{gathered}$$
• $\text{Under what condition are two lines (such as a tangent and a normal) considered perpendicular?}$
  $$\begin{gathered} \text{If the product of their gradients is }-1\text{.} \\ {m}_1\times m_2=-1 \\ \text{(Unless one is vertical and the other horizontal).} \end{gathered}$$