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

Question

Function
f(x) = 2x^2

Line
6x – y + 4 = 0

Answer 1

f'(x) = 4x
slope of given line = 6
so
4x = 6
x = 3/2
then y = 9/2

since new line is parallel to old line, it should look like
6x- y= K
plug in point (3/2, 9/2)
6(3/2) -9/2 =k
k = 9/2
so 6x - y = 9/2, or
12 - 2y = 9