find an equation of the line that is

Question

Find an equation of the line that is tangent to the graph of f and parallel to the given line.

Function		Line
f(x) = 2x2		4x − y + 5 = 0

Answer 1

The given line has a slope of 4 (determined after placing in slope intercept form is necessary, i.e. y = 4x+5. If you find f'(x) = 4x, which is a "formula" for slopes of tangent lines to the given function, you want the tangent line to also have a slope of 4 (parallel). Therefore 4x = 4 means x = 1. That is the x coordinate of the p.o.t. (point of tangency). The y coordinate of p.o.t. will be f(1) = 2.

Now we have a line passing through (1,2 ) with a slope of 4. Using point-slope:

y-2 = 4(x - 1). Convert to slope-intercept form is necessary.