Theory question 104
DifferentiationFind the equation of the tangent to the curve y = (x − 1)/(2x + 1), x ≠ −½, at the point (1, 0).
Show the model answer
Model answer
Quotient rule: dy/dx = [(2x + 1) − 2(x − 1)]/(2x + 1)² = 3/(2x + 1)²
At x = 1: gradient = 3/9 = 1/3
Tangent: y − 0 = ⅓(x − 1)
3y = x − 1, i.e. x − 3y − 1 = 0
Explanation
Find the gradient with the quotient rule, then use y − y₁ = m(x − x₁).