Question

Find the points on the curve y = `4x^3 - 3x + 5` at which the equation of the tangent is parallel to the x-axis.

Answer 1

`y = 4x^3 - 3x + 5 `...(i)

`dy/dx = 12x^2 - 3`

Given that lines is parallel to x-a xis

`:. dy/dx = 0`

`12x^2 - 3 = 0`

`12x^2 = 3`

`x^2 = 1/4`

`x= +- 1/2`

Put `x = +- 1/2` in equation (i)

`x = 1/2  "then " y = 4 (1/2)^3 - 3(1/2) + 5 = 4`

`:. "Point"(1/2, 4)`

when `x = (-1)/2`  then `y = 4 ((-1)/(2)) - 3((-1)/2) + 5 = 6`

:. Point (x,y) = `(1/2, 4)` and `((-1)/2, 6)`