Answer:
E) None of the above
Explanation:
y = 2x + 1 is the tangent line at x = 1, so f(1) = 3 and f'(1) = 2.
We also know that f(2) = 6, and that the tangent line passes through (2,5).
If we assume that f(x) doesn't change concavity between x=1 and x=2, then f(x) must be above the tangent line in that range, so f(x) is concave up.
An example would be f(x) = x² + 2.
However, we can't make that assumption. It's possible for f(x) to be concave up and concave down in that range.
An example would be f(x) = 3x³ − 11x² + 15x − 4.
Graph:
desmos.com/calculator/iidgm1o7xv
Therefore, there is not enough information to make any of these conclusions.