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) = 2x^2 2x − y + 5 = 0

Answer 1

the point is not to find the intersection of the curve and line

rather it is to find a **new line** which: (A) is a tangent line to f(x); and (B) runs parallel to 2x − y + 5 = 0

this means solving \(f'(x) = m\) where m is the slope of the line 2x − y + 5 = 0.

this should lead to a point \( (a, 2a^2)\) on the new line.

then finish off by using point \((a,2a^2)\) & slope m to solve \(y = mx + c\) for the new line