The tangent line to f(x) at x = c has slope equal to the derivative at c, or f'(c).
We have
f(x) = 3 - 2 x + 7 x²
so that
f'(x) = -2 + 14 x
The slope is 5 for
-2 + 14 x = 5 ==> 14 x = 7 ==> x = 1/2
Now, f (1/2) = 15/4, so the tangent line has equation
y - 15/4 = 5 (x - 1/2) ==> y = 5 x + 5/4
