anonymous
  • anonymous
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?
Mathematics
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anonymous
  • anonymous
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?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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
  • anonymous
the answer should be 2e
anonymous
  • anonymous
So I find the x-int and y-int using the derivative.

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anonymous
  • anonymous
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
  • anonymous
Okay thank you!
anonymous
  • anonymous
np medal me

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