A curve has equation $y=\frac{4}{3x-4}$ and $P$(2,2) is a point on the curve. Find the angle that this tangent makes with the x-axis.
Can anyone explain this ?
[Math] Tangent makes with the x-axis
algebra-precalculuscalculusgeometry
algebra-precalculuscalculusgeometry
A curve has equation $y=\frac{4}{3x-4}$ and $P$(2,2) is a point on the curve. Find the angle that this tangent makes with the x-axis.
Can anyone explain this ?
Best Answer
The angle is related to the slope of the tangent line at the point. Specifically, the slope is given by the derivative: \begin{equation} \begin{aligned} y' & = \left( \frac{4}{3x - 4} \right)' |_{x=2}\\ & = -\frac{12}{(3x -4)^2} |_{x=2}\\ & = -3 \end{aligned} \end{equation} which means $\tan \theta = -3$, so $\theta = \tan^{-1} (-3)$ is your angle.