Asked by MEG
What is the x-coordinate of the point on the curve y=e^x that is closest to the orgin?
Answers
Answered by
Reiny
Let the point of contact be P(x,y)
and the distance from the origin be D
D^2 = x^2 + y^2
= x^2 + e^(2x)
2D dD/dx = 2x + 2e^(2x)
= 0 for a min of D
so
x = -e^(2x) , a nasty equation to solve
I tried some trial and error, with 3 columns
x --- Right side
-.5 -.36
-.4 -.449
-.39 -.458
-.41 -.440
-.42 .4317
-.43 .4232
-.425 -.427
so x = appr. -.425
and the distance from the origin be D
D^2 = x^2 + y^2
= x^2 + e^(2x)
2D dD/dx = 2x + 2e^(2x)
= 0 for a min of D
so
x = -e^(2x) , a nasty equation to solve
I tried some trial and error, with 3 columns
x --- Right side
-.5 -.36
-.4 -.449
-.39 -.458
-.41 -.440
-.42 .4317
-.43 .4232
-.425 -.427
so x = appr. -.425
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