



 
Hi Elvina. The distance from the origin to any point (x,y) is simply sqrt(x^{2} + y^{2}) (you can see this by drawing a right triangle to it and using the Pythagorean Theorem). Therefore the distance d to the point (x,y) where y = e^{x} can be found by calculating
Note that d is always positive, so the smallest d means the smallest d^{2}. Thus you can ignore the d^{2} (i.e. we are ignoring the square root from earlier) and just evaluate df/dx where f(x) = x^{2} + e^{2x}. When you get this derivative, set it equal to zero and solve for x. This gives you the value of x at which y = e^{x} is closest to the origin. If you need further assistance write back. Cheers,  


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