<p>Given curve \(y = x^2 - 5x + 6\). The angle between the tangents drawn at the points \(x = 2\) and \(x = 3\) is</p>
Step-by-Step Solution
Key Concept: Find slopes of tangents at two points using derivatives, then use the angle formula tan(θ) = |(m₁ - m₂)/(1 + m₁m₂)| to find the angle between them.
<p><strong>Step 1:</strong> Find the derivative: y' = 2x - 5</p><p><strong>Step 2:</strong> Find slope at x = 2: m₁ = 2(2) - 5 = -1</p><p><strong>Step 3:</strong> Find slope at x = 3: m₂ = 2(3) - 5 = 1</p><p><strong>Step 4:</strong> Use angle formula: tan(θ) = |m₁ - m₂|/(1 + m₁m₂) = |(-1) - (1)|/(1 + (-1)(1)) = |-2|/(1 - 1) = 2/0</p><p><strong>Step 5:</strong> When denominator = 0, the tangents are perpendicular, so θ = 90°</p><p>∴ Answer: B (90° or π/2 radians)</p>
Correct Answer: B