If a ≥ 0, f (x) = x ^ 2 + ax, let x1 ∈ (- ∞, - A / 2) If a ≥ 0, f (x) = x ^ 2 + ax, let x1 ∈ (- ∞, - A / 2), let y = f (x) be tangent l at point m (x1, f (x1)), and let L and X axis intersection n (x2 (2 is subscript), 0), and o be origin It is proved that X2 (2 is subscript) ≤ X1 / 2 2. If the vector om * vector on > 9A / 16 holds for any x 1 ∈ (- ∞, - A / 2), the range of a is obtained | Math enthusiast | Mathematical art

If a ≥ 0, f (x) = x ^ 2 + ax, let x1 ∈ (- ∞, - A / 2) If a ≥ 0, f (x) = x ^ 2 + ax, let x1 ∈ (- ∞, - A / 2), let y = f (x) be tangent l at point m (x1, f (x1)), and let L and X axis intersection n (x2 (2 is subscript), 0), and o be origin It is proved that X2 (2 is subscript) ≤ X1 / 2 2. If the vector om * vector on > 9A / 16 holds for any x 1 ∈ (- ∞, - A / 2), the range of a is obtained

From F '(x) = 2x + A. so l linear equation y-x1 ^ 2-ax1 = (2x1 + a) (x-x1). Then it passes through n points (X2, O) and is replaced by x2 = X1 / (2-A / x1). Because a > = 0.x19a/16

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