Estimate Smallest Distance Between (0,0) and y=e^x

[erencan144]

"Using IVT and RT work out an estimate for the smallest distance between the point (0,0) and the curve
y = e^x "
Can anyone help me with this question? Thanks.


Note: IVT is "Intermediate Value Theorem" and RT is "Rolle's Theorem"

 

[rochfor1]

What is the function for distance between the points (0,0) and (x,e^x)?

 

[mathman]

d²=x²+e^2x

RT says there is a point where the tangent (to d²) is horizontal, since the function ->+∞ for both x and -x ->∞. This would be the minimum.

Use IVT on the derivative of x² let's you find the minimum (0 derivative), since the derivative goes to +∞ as x goes to +∞, while it goes to -∞ as x goes to -∞.