Find k such that the line is tangent to the graph of the function. Function Line f(x) = k x y = 2x + 18 k =

Question

Find k such that the line is tangent to the graph of the function.

Function	Line	f(x) = k	x
	y = 2x + 18

k = 

Answer 1

Let the point on the graph of f be represented by (x, k√x). The given line passes through the point (0,18) with a slope of 2.

You can come up with two equations for the slope. One using the two points and another using the fact that the derivative of f(x) at the point where y = 2x+18 is tangent will also have a slope of 2.

So,

(k√x-18)/(x-0) = 2 (slope calculated using the two points.

1/2 (k) /√x = 2 (the derivative also equals 2)=> k = 4√x. Substitute that value into the 1st equation and solve for x. That will be the x -coordinate of the POT (point of tangency). Substitute that value into either equation to find the required value for k.