Answer to Question #18723 in Calculus for hsd

Question

Consider the function f(x)=2x+5.

If D is the distance from any point on f(x) to the origin:
D=

At what x value is f(x) closest to the origin?
x=

Answer 1

let A point on f(x) then it have coordinates (x, 2x+5)and we must find distance from this point to (0, 0) D=sqrt( x^2+(2x+5)^2)=sqrt(5x^2+20x+25)
min value at vertex of 5x^2+20x+25 x=-2