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Application of Derivatives

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Long Answer Type

111.

Find the equation of the tangent line to the curve y = x² – 2x + 7 which is
(a) parallel to the line 2x – y + 9 = 0
(ii) perpendicular to the line 5y – 15y = 13

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112. Find the equations of normal lines to the curve y = x² – 3 x which are parallel to the line x + 9y = 14.

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113. Find the equation of the normals to the curve y = x³ + 2x + 6 which are parallel to the line 14y + 4 = 0.

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114.

At what point will the tangent to the curve y = 2x³ – 15x² + 36x – 21 be parallel to x-axis ? Also, find the equations of tangents to the curve at those points.

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Short Answer Type

115.

Find the points on the curve x² + y² -2x – 3 = 0 at which the tangents are parallel to the x-axis.

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116. Find points at which the tangent to the curve y = x³ – 3x² – 9x + 7 is parallel to the x-axis.

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117.
Find point on the curve y = 3x² – 12x + 6 at which tangent is parallel to x-axis. Also find the equation of tangent line.

The equation of curve is
y = 3x² – 12x + 6 ...(1)
$therefore space space space space space space dy over dx space equals space 6 straight x minus 12 because space space space space space tangent space is space parallel space to space straight x minus axis therefore space space space space space space dy over dx space equals space 0 space space space space space space space space space space space space space space rightwards double arrow space space space space 6 straight x minus 12 space equals space 0 space space space space rightwards double arrow space space space straight x space equals space 2 Putting space space straight x space equals space 2 space in space left parenthesis 1 right parenthesis comma space we space get comma space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight y equals 12 minus 24 plus 6 space equals space minus 6 therefore space space space space space space point space is space left parenthesis 2 comma space minus 6 right parenthesis The space equation space of space tangent space line space is space straight y space equals space minus 6$

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118.

Find out on the curve y = x² – x – 8 at which tangent is parallel to x-axis. Also find the equation of tangent line.

81 Views

119.

Find out on the curve y = 2 x² – 6x – 4 at which tangent is parallel to x-axis. Also find the equation of tangent line.

74 Views

Long Answer Type

120.

Find out the points on the curve $straight x squared over 9 minus straight y squared over 16 space equals space 1$ at which the tangents are (i) parallel to the x-axis and (ii) parallel to the y-axis.