Let . How many real solutions does the equation have?
Answer and explanation
Correct answer: A. 7
- Step 1: Analyze : the derivative has critical points at (local maximum ) and (local minimum ).
- Step 2: By the Intermediate Value Theorem, has three real roots: , , and .
- Step 3: The equation implies . For any value , has real solutions if , and real solution if or . Since , it contributes solution; since , they contribute solutions each. Thus, total solutions are .
Answer
7.
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