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?

Question

anonymous · Answer

Take the derivative of the function.. you will get -e^(2-x)
Put one in the 1, you will get -e. This is the slope of your tangent
Now find the x and y intercepts, and use the 1/2 (xint) * (yint)
You will get area.

anonymous · Answer

the answer should be 2e

anonymous · Answer

So I find the x-int and y-int using the derivative.

anonymous · Answer

you set up the equation as y = -ex + b
and first you plug in 1 as x and e as y, to get b, which is your y intercept,
and then you use the new equation -ex+2e =y and set y to 0, which well give x = 2, your x int

anonymous · Answer

Okay thank you!

anonymous · Answer

np medal me