Question

The tangent line to the graph y=e^(2-x) at the point (1,e) intersects both coordinate axes. What is the areas of the triangle formed by this tangent line and the coordinate axes?

Answer 1

The formula for the tangent line of a function \(f(x)\) at the point \((a, f(a))\) is given by:\[
y-f(a) = f'(a)(x-a)
\]
Given that \(a=1\) and \(f(a)=e\)\[
y-e = f'(1)(x-1)
\]

Answer 2

So first let's find the tangent line.