Explanation
Correct answer: B.
Choice B is the best answer. "Asserted" means "stated confidently." Eastlake "did not hesitate to publish reviews going against popular opinion," so we can assume that she was confident in sharing her opinions.
Why the other choices are wrong
Choice A
Choice A is incorrect. "Exposed" means "made visible by uncovering" and, when talking about ideas, tends to be used in relation to uncovering the truth. Eastlake was sharing an opinion, not uncovering a truth.
Choice C
Choice C is incorrect. "Discovered" means "found," but Eastlake was writing an opinion essay. She was writing her own opinion, not "discovering" a new universal truth.
Choice D
Choice D is incorrect. "Doubted" means "didn’t believe in." We’re told that Eastlake "questioned" the idea that photography could be fine art. Placing "doubted" in the blank would actually suggest that Eastlake argued that photos were valuable for creativity and not for information, which is the opposite of what we were told she believes.