Consider the curve x = e^t, y = e^-t. At the point (1/3, 3), an equation of the tangent line is y = [m]x + [b]. What is "m" and "b"?

Question

anonymous · Answer

$m$ and $b$ are the slope and y-intercept of the tangent line, respectively. Judging by the notation, $[m]$ and $[b]$, which usually are used to indicate the integer part of $m$ and $b$, you want an approximated tangent line to the given curve.

You can find the slope $[m]$ by differentiating the parametric curve at the given point $\left(\dfrac{1}{3},3\right)$, and $[b]$ by using the point slope formula for lines.