Question

The point at which the tangent to the curve y = 2x² - x + 1 is parallel to y = 3x + 9 will be

(A) (2, 1)

(B) (1, 2)

(C) (3, 9)

(D) (−2, 1)

Answer 1

Answer is (B) (1, 2)

We have

y = 2x² - x + 1 ⇒ dy/dx = 4x - 1

We know that this equation gives the slope of tangent to the curve. Since this tangent is parallel to y = 3x + 9, the slope of the tangent is 3 and so 4x - 1= 3 or x =1. Therefore y = 2x² - x + 1 = 2. Thus, the point (x, y) is (1, 2).