ISC (Science) Class 12CISCE
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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

#### 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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