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Find the Points on the Curve Y = `4x^3 - 3x + 5` at Which the Equation of the Tangent is Parallel to the X-axis. - ISC (Science) Class 12 - Mathematics

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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.

Solution

`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)`

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Solution Find the Points on the Curve Y = `4x^3 - 3x + 5` at Which the Equation of the Tangent is Parallel to the X-axis. Concept: Tangents and Normals.
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