Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Application of Derivatives

Name: Zigya - For The Curious Learner
Rating: 4.4 (740 reviews)

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

75 Views

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

73 Views

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

74 Views

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.

132 Views

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.

The equation of curve is x² + y² -2x – 3 = 0 ...(1)
Differentiating both sides, w.r.t.x, we get,
$2 straight x plus 2 straight y dy over dx minus 2 minus 0 space equals space 0 comma space space space space or space space space 2 straight y dy over dx space equals space minus 2 straight x plus 2 therefore space space space space space space dy over dx space equals space fraction numerator negative straight x plus 1 over denominator straight y end fraction because space space space space space dy over dx space equals space 0 space space space space rightwards double arrow space space space space space space fraction numerator negative straight x plus 1 over denominator straight y end fraction space equals space 0 space space space space rightwards double arrow space space space straight x space equals 1 comma space space space space straight y not equal to 0 Putting space straight x space equals space 1 space in space left parenthesis 1 right parenthesis comma space we space get comma space space space space space space space space space space space space space space space space space space space space space space 1 plus straight y squared minus 2 minus 3 space equals space 0 comma space space space space or space space space space straight y squared space equals space 4 space space space space rightwards double arrow space space space space straight y space equals space minus 2 comma space space space 2 therefore space space space space space space space space pionts space left parenthesis 1 comma space minus 2 right parenthesis comma space space left parenthesis 1 comma space 2 right parenthesis.$

72 Views

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

93 Views

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.

74 Views

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.