Question

The derivative (or slope fo the tangent line to f(x) )at x = 2 is -3/4. Find the slope of the normal at x =2

Answer 1

TThe normal line is a line perpendicular to the tangent line at a certain point of tangency, in this case at x=2.

Two lines are perpendicular when the product between the slopes of both is equal to -1.

then,

`m_1\ast m_2=-1`

The slope for the tangent line is given, then,

`\begin{gathered} -(3)/(4)\ast m_2=-1 \\ \end{gathered}`

clear for the slope of the normal

`\begin{gathered} m_2=-1\ast(-(4)/(3)) \\ m_2=(4)/(3) \end{gathered}`

Answer:

The slope of the normal at x=2 is 4/3.