Mathematics · Calculus
Let f: (a, b) → R be a twice differentiable function such that f(x) = ∫ax g(t) dt for a differentiable function g(x). If f(x) = 0 has exactly five distinct roots in (a, b), then g(x)g'(x) = 0 has at least:
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- 1three roots in (a, b)
- 2seven roots in (a, b)✓
- 3five roots in (a, b)
- 4twelve roots in (a, b)
Correct answer
seven roots in (a, b)
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