Question

Consider a triangle in the first quadrant formed by the
coordinate axes and a tangent to the curve with the equation y=e^(-x) .
Find the maximum area of the triangle.

Answer 1

ok, lets use calculus to solve it. first we need to find the area in function of x

Answer 2

let say x is the coordinate in which we take the tangent, so we would now need to calculate the intersaction coordinates

Answer 3

So would we isolate x?

Answer 4

\[y=e ^{-X0}-(x-X0)e ^{-X0}\] is the function for the tangent,

Answer 5

we need to get the values of x and y for both intersections, also put y=0, and x=0 in that equation

Answer 6

ah! okay :)

Answer 7

so \[\Delta y = e ^{-X0} \times (1+X0)\]