For every twice differentiable function f : R [–2, 2] with (f(0))2 + (f(0))2 = 85, which of the following statement(s) is (are) TRUE?(A) There exist r, s R, where r (B) There exists x0 (–4, 0) such that |f(x0)| 1(C) xlim f(x) 1(D) There exists (–4, 4) such that f() + f() = 0 and f() 0
Mineesh reddy , 6 Years ago
Grade 12
1 Answers
Arun
Last Activity: 6 Years ago
L.M.V.T. in [–4, 0]
|f'(x1)| ≤ 1 for some x1 ∈ (0, 4)
g(x) = (f(x))2 + (f'(x))2 g(x0) ≤ 5, g(x1) ≤ 5 g(0) = 85 it has a local maximum having value ≥ 85 Say α g'(α) = 0, g''(α) ≤ 0 2f(α)f'(α) + 2f'(α)f''(α) = 0 f'(α)(f(α) + f'(α)) = 0 as f'(α) ≠ 0
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