Question

Consider the curve y = x² – 2x + 7

1. Find the slope of the tangent of the curve at x = 2. 

2. Write down the equation of the tangent at x =2. 

Answer 1

1. Given,

y = x² – 2x + 7 ⇒ y’ = 2x – 2

(y’)_x=2 = 2(2) – 2 = 2.

2. At x = 2 , y = 2² – 2(2) + 7 = 7.

Equation of the tangent at (2, 7) is

y – 7 = 2(x – 2) ⇒ 2x – y + 3 = 0.