Question

Find the point on the curve y = 2x² – 6x – 4 at which the tangent is parallel to the x-axis.

Answer 1

y = 2x² – 6x – 4   ...(1)

Differentiate w.r.t. x, we get

`(dy)/(dx) = 4x - 6`

Given, tangent is parallel to x-axis.

`(dy)/(dx) = 0`

⇒ 4x – 6 = 0

⇒ `x = 3/2`

Substitute the value of x in equation (i), we get

`y = 2(3/2)^2 - 6(3/2) - 4`

⇒ `y = 2 xx 9/4 - 18/2 - 4`

⇒ `y = (-17)/2`

Points are `(3/2, (-17)/2)`