Find an equation of the line that is tangent to the graph of f and parallel to the given line. Function f(x) = 2x2 and line 2x − y + 5 = 0

Answer 1

The tangent must have slope 2.

dy/dx = 4x = 2 => x=1/2

At x=1/2, y=1/2.

The tangent line then is 2 = [y-(1/2)]/[x-(1/2)]

and this equation may be "massaged" into any required form.