Answer:
the first answer y = 20x - 15
Explanation:
since the correct tangent line must share the same point with the originated function, only a line function that delivers y = 25 for x = 2 can be correct.
only the first answer option provides this (20×2 - 15 = 25).
so, we know, this line goes through the given point, but does it have the correct slope for the tangent ?
the correct slope we get from the first derivative of the original function.
f(x) = (1 + 2x)² = 1 + 4x + 4x²
f'(x) = 4 + 8x
for x = 2 we get the tangent slope at that point as
4 + 8×2 = 20
and the provided line is again
y = 20x - 15
with the slope being the factor of x (20).
so, it fits, and indeed, answer 1 is correct.